CBSE Class 8 > Class 8 Videos > Mathematics (Maths) > Area of Trapezium & General Quadrilateral
Area of Trapezium & General Quadrilateral Video Lecture - (Maths) Class
Text Transcript from Video
0:0:0: in this video we will discuss the area
0:0:2: of a trapezium and area of a general
0:0:5: quadrilateral you already know from your
0:0:7: previous classes that the area measures
0:0:10: how much space a shape covers and
0:0:12: perimeter is the outline distance around
0:0:14: it just like when you're laying out a
0:0:17: picture frame the glass inside is the
0:0:21: area while the frame itself is a
0:0:24: perimeter before starting with the main
0:0:26: topics of the video Let's see a quick
0:0:29: recap of some common shapes and their
0:0:31: areas and perimeter in rectangles area
0:0:35: is equal to length time width and
0:0:37: perimeter is equal to sum of all sides
0:0:40: for squares since all sides are equal
0:0:43: area is equal to Side Square and
0:0:46: perimeter is equal to 4 * side in
0:0:49: circles here the area is equal to P piun
0:0:52: r² where Pi is approximately 3.14 and R
0:0:56: is the radius of the circle and the
0:0:58: circumference is equal to 2
0:1:1: pi in triangles area is equal to half *
0:1:5: base time height for parallelograms area
0:1:8: is equal to base time height got all
0:1:12: that great you're already familiar with
0:1:16: these
0:1:17: Concepts so let's start something new
0:1:20: have you ever seen a
0:1:22: trapezium a trapezium is like a
0:1:25: rectangle with one corner cut off
0:1:27: creating a slanted side this is done by
0:1:30: removing a triangle from one corner of
0:1:32: the rectangle parallel to its base books
0:1:36: will tell you that the area of trapezium
0:1:38: is half the sum of the parallel sides
0:1:40: times the height but how did we derive
0:1:43: this
0:1:44: formula let's see for ourselves using an
0:1:47: example meet nazma who has a beautiful
0:1:51: plot of land she wants to cover her plot
0:1:54: of land with grass but there is one
0:1:56: problem unlike the rectangular plots in
0:1:58: her neighborhood najma's plot looks
0:2:1: different because it has just one pair
0:2:3: of parallel sides making it a
0:2:6: trapezium and she does not know how to
0:2:8: find its
0:2:9: area to find out how much space nazma's
0:2:13: plot covers let's first label the
0:2:15: corners of her plot as abde we will
0:2:18: first draw a line EC parallel to the
0:2:20: side AB this clever move splits the plot
0:2:24: into two familiar shapes a rectangle
0:2:26: abce e and a right angle triangle ecd
0:2:30: remember the area of a rectangle is
0:2:33: length time width and the area of a
0:2:35: triangle is half time base time height
0:2:38: let's use these formulas to find the
0:2:41: area for njma plot step one calculate
0:2:45: the area of triangle
0:2:47: ecd for the triangle we use the formula
0:2:51: half * base time height here the base C
0:2:55: is 10 m and the height H is 12
0:2:58: m so the area of triangle ecd is half *
0:3:4: 10 * 12 is = 60
0:3:7: m² step two calculate the area of
0:3:10: rectangle abce e now for the rectangle
0:3:14: abce the formula is length time width
0:3:18: the length a is 20 M and the width H is
0:3:21: also 12
0:3:22: M thus the area of the rectangle is 20 *
0:3:27: 12 is equal to 24 4 M squared by
0:3:32: combining the area of the triangle and
0:3:34: the rectangle najma finds that her plot
0:3:37: covers 60 m² + 40 m² is equal to 300 M
0:3:43: squ of space that's the size of her
0:3:46: trapezium shaped plot we can also write
0:3:49: the area by combining the two areas and
0:3:52: write the area of trapezium abde e is
0:3:57: equal to half * H * C
0:4:0: plus h * a which can be resolved further
0:4:4: as shown in these
0:4:6: steps now from the figure we can see
0:4:9: that a + C is equal to B so we can write
0:4:12: the formula as area of trapezium is
0:4:14: equal to H * A + B / 2 or sum of
0:4:20: parallel sides time height divided by 2
0:4:25: again by substituting the values of h b
0:4:28: and a in this expression we find the
0:4:30: area is equal to 300 M squared and there
0:4:34: you have it we have calculated the area
0:4:37: of trapezium field plot using the
0:4:39: derived
0:4:41: formula now let us see how do we
0:4:43: calculate the area of a general
0:4:46: quadrilateral unlike the shapes we've
0:4:48: met before this one doesn't have sides
0:4:51: which we can easily measure to find its
0:4:53: area but don't worry with a bit of work
0:4:56: we can solve this as well here we have
0:5:0: taken a general quadrilateral AB c d now
0:5:3: let's see how to calculate its area step
0:5:7: one use of the diagonal join the points
0:5:11: A and C making the diagonal a c this
0:5:14: line splits our quadrilateral into two
0:5:16: triangles ABC and
0:5:18: ADC this diagonal will pave the way for
0:5:21: us to calculate the area of a
0:5:24: quadrilateral step two calculating the
0:5:27: area of triangles recall students the
0:5:31: area of a triangle is half the base
0:5:33: times the height our base for both
0:5:36: triangles is a diagonal AC let's call
0:5:40: The Heights from the base to the
0:5:41: opposite vertices H1 for triangle
0:5:44: ABC and H2 for triangle
0:5:48: ADC step three adding up the areas to
0:5:53: uncover the total area of our
0:5:55: quadrilateral we simply add the areas of
0:5:57: our two triangles
0:6:0: that's half * AC * H1 for the first
0:6:4: triangle plus half * AC * H2 for the
0:6:8: second adding them up gives us half * AC
0:6:13: * H1 +
0:6:15: H2 finally we have got the area formula
0:6:19: so the area of our quadrilateral AB c d
0:6:21: is half * D * H1 + H2 where D is the
0:6:26: length of our diagonal AC and H1 and H2
0:6:29: are the heights to this diagonal from
0:6:31: the opposite
0:6:32: vertices let's try to solve an example
0:6:35: using this
0:6:36: formula the diagonal of a quadrilateral
0:6:39: shaped field is 24 M and the
0:6:41: perpendiculars dropped on it from the
0:6:43: remaining opposite vertices are 8 m and
0:6:46: 13 M find the area of the field let us
0:6:50: first draw a figure for this question
0:6:53: now from the figure we can see that H1
0:6:56: is equal to 13 M H2 is equal to 8 m and
0:7:0: the diagonal D is equal to 24 M now
0:7:4: putting these values in the formula that
0:7:6: we derived previously we get that area
0:7:10: of quadrilateral is equal to half * 24 *
0:7:13: 13 + 8 is equal to half * 24 *
0:7:19: 21 is equal to 252 M
0:7:22: squar so the area of a quadrilateral
0:7:25: shaped field is 252 M squared
0:7:30: let us now have a brief recap of what we
0:7:32: have studied so far we Revisited
0:7:35: fundamental shapes reviewing their
0:7:37: respective areas and
0:7:39: perameters subsequently we delved into
0:7:42: deriving the formula for calculating the
0:7:45: area of a
0:7:46: trapezium additionally we explored
0:7:49: methods for determining the area of a
0:7:51: quadrilateral and derived its formula to
0:7:54: discover more about such topics check
0:7:57: out the urv app it offers video lessons
0:8:0: chapter summaries and quizzes designed
0:8:3: to help you understand these Concepts
0:8:5: better you can also find engaging
0:8:8: courses on subjects like Science Social
0:8:11: Studies English Hindi and more
0:0:2: of a trapezium and area of a general
0:0:5: quadrilateral you already know from your
0:0:7: previous classes that the area measures
0:0:10: how much space a shape covers and
0:0:12: perimeter is the outline distance around
0:0:14: it just like when you're laying out a
0:0:17: picture frame the glass inside is the
0:0:21: area while the frame itself is a
0:0:24: perimeter before starting with the main
0:0:26: topics of the video Let's see a quick
0:0:29: recap of some common shapes and their
0:0:31: areas and perimeter in rectangles area
0:0:35: is equal to length time width and
0:0:37: perimeter is equal to sum of all sides
0:0:40: for squares since all sides are equal
0:0:43: area is equal to Side Square and
0:0:46: perimeter is equal to 4 * side in
0:0:49: circles here the area is equal to P piun
0:0:52: r² where Pi is approximately 3.14 and R
0:0:56: is the radius of the circle and the
0:0:58: circumference is equal to 2
0:1:1: pi in triangles area is equal to half *
0:1:5: base time height for parallelograms area
0:1:8: is equal to base time height got all
0:1:12: that great you're already familiar with
0:1:16: these
0:1:17: Concepts so let's start something new
0:1:20: have you ever seen a
0:1:22: trapezium a trapezium is like a
0:1:25: rectangle with one corner cut off
0:1:27: creating a slanted side this is done by
0:1:30: removing a triangle from one corner of
0:1:32: the rectangle parallel to its base books
0:1:36: will tell you that the area of trapezium
0:1:38: is half the sum of the parallel sides
0:1:40: times the height but how did we derive
0:1:43: this
0:1:44: formula let's see for ourselves using an
0:1:47: example meet nazma who has a beautiful
0:1:51: plot of land she wants to cover her plot
0:1:54: of land with grass but there is one
0:1:56: problem unlike the rectangular plots in
0:1:58: her neighborhood najma's plot looks
0:2:1: different because it has just one pair
0:2:3: of parallel sides making it a
0:2:6: trapezium and she does not know how to
0:2:8: find its
0:2:9: area to find out how much space nazma's
0:2:13: plot covers let's first label the
0:2:15: corners of her plot as abde we will
0:2:18: first draw a line EC parallel to the
0:2:20: side AB this clever move splits the plot
0:2:24: into two familiar shapes a rectangle
0:2:26: abce e and a right angle triangle ecd
0:2:30: remember the area of a rectangle is
0:2:33: length time width and the area of a
0:2:35: triangle is half time base time height
0:2:38: let's use these formulas to find the
0:2:41: area for njma plot step one calculate
0:2:45: the area of triangle
0:2:47: ecd for the triangle we use the formula
0:2:51: half * base time height here the base C
0:2:55: is 10 m and the height H is 12
0:2:58: m so the area of triangle ecd is half *
0:3:4: 10 * 12 is = 60
0:3:7: m² step two calculate the area of
0:3:10: rectangle abce e now for the rectangle
0:3:14: abce the formula is length time width
0:3:18: the length a is 20 M and the width H is
0:3:21: also 12
0:3:22: M thus the area of the rectangle is 20 *
0:3:27: 12 is equal to 24 4 M squared by
0:3:32: combining the area of the triangle and
0:3:34: the rectangle najma finds that her plot
0:3:37: covers 60 m² + 40 m² is equal to 300 M
0:3:43: squ of space that's the size of her
0:3:46: trapezium shaped plot we can also write
0:3:49: the area by combining the two areas and
0:3:52: write the area of trapezium abde e is
0:3:57: equal to half * H * C
0:4:0: plus h * a which can be resolved further
0:4:4: as shown in these
0:4:6: steps now from the figure we can see
0:4:9: that a + C is equal to B so we can write
0:4:12: the formula as area of trapezium is
0:4:14: equal to H * A + B / 2 or sum of
0:4:20: parallel sides time height divided by 2
0:4:25: again by substituting the values of h b
0:4:28: and a in this expression we find the
0:4:30: area is equal to 300 M squared and there
0:4:34: you have it we have calculated the area
0:4:37: of trapezium field plot using the
0:4:39: derived
0:4:41: formula now let us see how do we
0:4:43: calculate the area of a general
0:4:46: quadrilateral unlike the shapes we've
0:4:48: met before this one doesn't have sides
0:4:51: which we can easily measure to find its
0:4:53: area but don't worry with a bit of work
0:4:56: we can solve this as well here we have
0:5:0: taken a general quadrilateral AB c d now
0:5:3: let's see how to calculate its area step
0:5:7: one use of the diagonal join the points
0:5:11: A and C making the diagonal a c this
0:5:14: line splits our quadrilateral into two
0:5:16: triangles ABC and
0:5:18: ADC this diagonal will pave the way for
0:5:21: us to calculate the area of a
0:5:24: quadrilateral step two calculating the
0:5:27: area of triangles recall students the
0:5:31: area of a triangle is half the base
0:5:33: times the height our base for both
0:5:36: triangles is a diagonal AC let's call
0:5:40: The Heights from the base to the
0:5:41: opposite vertices H1 for triangle
0:5:44: ABC and H2 for triangle
0:5:48: ADC step three adding up the areas to
0:5:53: uncover the total area of our
0:5:55: quadrilateral we simply add the areas of
0:5:57: our two triangles
0:6:0: that's half * AC * H1 for the first
0:6:4: triangle plus half * AC * H2 for the
0:6:8: second adding them up gives us half * AC
0:6:13: * H1 +
0:6:15: H2 finally we have got the area formula
0:6:19: so the area of our quadrilateral AB c d
0:6:21: is half * D * H1 + H2 where D is the
0:6:26: length of our diagonal AC and H1 and H2
0:6:29: are the heights to this diagonal from
0:6:31: the opposite
0:6:32: vertices let's try to solve an example
0:6:35: using this
0:6:36: formula the diagonal of a quadrilateral
0:6:39: shaped field is 24 M and the
0:6:41: perpendiculars dropped on it from the
0:6:43: remaining opposite vertices are 8 m and
0:6:46: 13 M find the area of the field let us
0:6:50: first draw a figure for this question
0:6:53: now from the figure we can see that H1
0:6:56: is equal to 13 M H2 is equal to 8 m and
0:7:0: the diagonal D is equal to 24 M now
0:7:4: putting these values in the formula that
0:7:6: we derived previously we get that area
0:7:10: of quadrilateral is equal to half * 24 *
0:7:13: 13 + 8 is equal to half * 24 *
0:7:19: 21 is equal to 252 M
0:7:22: squar so the area of a quadrilateral
0:7:25: shaped field is 252 M squared
0:7:30: let us now have a brief recap of what we
0:7:32: have studied so far we Revisited
0:7:35: fundamental shapes reviewing their
0:7:37: respective areas and
0:7:39: perameters subsequently we delved into
0:7:42: deriving the formula for calculating the
0:7:45: area of a
0:7:46: trapezium additionally we explored
0:7:49: methods for determining the area of a
0:7:51: quadrilateral and derived its formula to
0:7:54: discover more about such topics check
0:7:57: out the urv app it offers video lessons
0:8:0: chapter summaries and quizzes designed
0:8:3: to help you understand these Concepts
0:8:5: better you can also find engaging
0:8:8: courses on subjects like Science Social
0:8:11: Studies English Hindi and more
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Feb 17, 2026 Last updated
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