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All questions of Area for Class 8 Exam
How is the area of a trapezium different from that of a rectangle?- a)Trapezium has different heights
- b)Trapezium has only one base
- c)Trapezium has two parallel sides
- d)Rectangle has no height
Correct answer is option 'C'. Can you explain this answer?
How is the area of a trapezium different from that of a rectangle?
a)
Trapezium has different heights
b)
Trapezium has only one base
c)
Trapezium has two parallel sides
d)
Rectangle has no height
 | Ipsita Kulkarni answered |
Understanding the Trapezium and Rectangle
The area of a trapezium (or trapezoid) is calculated differently than that of a rectangle, primarily due to their structural characteristics.
Key Differences in Shape
- Trapezium has Two Parallel Sides:
A trapezium features one pair of parallel sides, known as the bases. This unique property distinguishes it from a rectangle, where both pairs of opposite sides are parallel.
- Rectangle has Four Right Angles:
In a rectangle, all angles are right angles (90 degrees), which allows for straightforward calculations of area using the formula: Area = Length × Width.
Area Calculation
- Area of a Trapezium:
The area of a trapezium is calculated using the formula:
Area = 1/2 × (Base1 + Base2) × Height.
This formula incorporates the lengths of both bases and the height, reflecting the trapezium's unique shape.
- Area of a Rectangle:
The area of a rectangle is simply:
Area = Length × Width.
Since rectangles have consistent lengths and widths, the calculation is more straightforward.
Conclusion
In summary, the primary difference that leads to distinct area calculations lies in the trapezium's two parallel sides, which creates a varying shape and necessitates a different formula for area. The rectangle's uniform shape, on the other hand, allows for a simpler area calculation. Understanding these differences is key to mastering geometry concepts at the Class 8 level.
The area of a trapezium (or trapezoid) is calculated differently than that of a rectangle, primarily due to their structural characteristics.
Key Differences in Shape
- Trapezium has Two Parallel Sides:
A trapezium features one pair of parallel sides, known as the bases. This unique property distinguishes it from a rectangle, where both pairs of opposite sides are parallel.
- Rectangle has Four Right Angles:
In a rectangle, all angles are right angles (90 degrees), which allows for straightforward calculations of area using the formula: Area = Length × Width.
Area Calculation
- Area of a Trapezium:
The area of a trapezium is calculated using the formula:
Area = 1/2 × (Base1 + Base2) × Height.
This formula incorporates the lengths of both bases and the height, reflecting the trapezium's unique shape.
- Area of a Rectangle:
The area of a rectangle is simply:
Area = Length × Width.
Since rectangles have consistent lengths and widths, the calculation is more straightforward.
Conclusion
In summary, the primary difference that leads to distinct area calculations lies in the trapezium's two parallel sides, which creates a varying shape and necessitates a different formula for area. The rectangle's uniform shape, on the other hand, allows for a simpler area calculation. Understanding these differences is key to mastering geometry concepts at the Class 8 level.
Which statement is always true?A) Larger perimeter means larger area
B) Same perimeter means same area
C) Same base and height means same area (for triangles)
D) Area depends only on perimeter- a)D
- b)C
- c)B
- d)A
Correct answer is option 'B'. Can you explain this answer?
Which statement is always true?
A) Larger perimeter means larger area
B) Same perimeter means same area
C) Same base and height means same area (for triangles)
D) Area depends only on perimeter
B) Same perimeter means same area
C) Same base and height means same area (for triangles)
D) Area depends only on perimeter
a)
D
b)
C
c)
B
d)
A
 | Naina Ahuja answered |
Understanding the Statements
To determine which statement is always true, let's analyze each option carefully.
A) Larger perimeter means larger area
- This statement is false. Different shapes can have the same perimeter but vastly different areas. For example, a long, thin rectangle can have the same perimeter as a compact square but will have a smaller area.
B) Same perimeter means same area
- This statement is also false. Different shapes can have the same perimeter but different areas. For instance, two different rectangles with the same perimeter can have varying lengths and widths, leading to differing areas.
C) Same base and height means same area (for triangles)
- This statement is true. For triangles, if the base and height are identical, the area will always be the same, regardless of the triangle's shape. The area of a triangle is calculated using the formula (1/2) * base * height.
D) Area depends only on perimeter
- This statement is false. Area is influenced by the dimensions of a shape and not solely by its perimeter. Two shapes can have the same perimeter but different areas, as previously mentioned.
Conclusion
Among the options provided, the correct and always true statement is:
- C) Same base and height means same area (for triangles)
This statement accurately reflects the fundamental property of triangles, ensuring consistency in area calculations based on these dimensions.
To determine which statement is always true, let's analyze each option carefully.
A) Larger perimeter means larger area
- This statement is false. Different shapes can have the same perimeter but vastly different areas. For example, a long, thin rectangle can have the same perimeter as a compact square but will have a smaller area.
B) Same perimeter means same area
- This statement is also false. Different shapes can have the same perimeter but different areas. For instance, two different rectangles with the same perimeter can have varying lengths and widths, leading to differing areas.
C) Same base and height means same area (for triangles)
- This statement is true. For triangles, if the base and height are identical, the area will always be the same, regardless of the triangle's shape. The area of a triangle is calculated using the formula (1/2) * base * height.
D) Area depends only on perimeter
- This statement is false. Area is influenced by the dimensions of a shape and not solely by its perimeter. Two shapes can have the same perimeter but different areas, as previously mentioned.
Conclusion
Among the options provided, the correct and always true statement is:
- C) Same base and height means same area (for triangles)
This statement accurately reflects the fundamental property of triangles, ensuring consistency in area calculations based on these dimensions.
What is the formula used to calculate the area of a rectangle?- a)Length × Width
- b)Length + Width
- c)Length ÷ Width
- d)Length - Width
Correct answer is option 'A'. Can you explain this answer?
What is the formula used to calculate the area of a rectangle?
a)
Length × Width
b)
Length + Width
c)
Length ÷ Width
d)
Length - Width
 | Nidhi Bhatt answered |
Let the rectangle have length L and width W.
Area = Length × Width = L × W.
Therefore the correct option is A.
How many square units are in the area of a rectangle with dimensions of 8 cm and 3 cm?- a)32 sq. cm
- b)24 sq. cm
- c)28 sq. cm
- d)11 sq. cm
Correct answer is option 'B'. Can you explain this answer?
a)
32 sq. cm
b)
24 sq. cm
c)
28 sq. cm
d)
11 sq. cm
| | Nidhi Bhatt answered |
Area of a rectangle = length × width.
Here, length = 8 cm and width = 3 cm, so area = 8 × 3 = 24 sq. cm.
What is the area of a triangle with a base of 5 units and a height of 3 units?- a)10 sq. units
- b)5 sq. units
- c)15 sq. units
- d)7.5 sq. units
Correct answer is option 'D'. Can you explain this answer?
a)
10 sq. units
b)
5 sq. units
c)
15 sq. units
d)
7.5 sq. units
| | Nidhi Bhatt answered |
Area of a triangle = 1/2 × base × height.
Substitute values: 1/2 × 5 × 3 = (1/2) × 15 = 7.5.
Therefore, the area is 7.5 sq. units.
The area of a trapezium with parallel sides 6 cm and 10 cm and height 4 cm is:- a)32 cm2
- b)40 cm2
- c)64 cm2
- d)80 cm2
Correct answer is option 'C'. Can you explain this answer?
The area of a trapezium with parallel sides 6 cm and 10 cm and height 4 cm is:
a)
32 cm2
b)
40 cm2
c)
64 cm2
d)
80 cm2
| | Nidhi Bhatt answered |
Area of trapezium = ½ × h × (sum of parallel sides)
= ½ × 4 × (6 + 10)
= 2 × 16 =
= ½ × 4 × (6 + 10)
= 2 × 16 =
64 cm2
If a trapezium has bases of 4 cm and 6 cm and a height of 5 cm, what is its area?- a)15 sq. cm
- b)25 sq. cm
- c)20 sq. cm
- d)30 sq. cm
Correct answer is option 'B'. Can you explain this answer?
If a trapezium has bases of 4 cm and 6 cm and a height of 5 cm, what is its area?
a)
15 sq. cm
b)
25 sq. cm
c)
20 sq. cm
d)
30 sq. cm
| | Nidhi Bhatt answered |
Area of a trapezium = (sum of parallel sides ÷ 2) × height.
Substitute: (4 + 6) ÷ 2 = 10 ÷ 2 = 5.
So area = 5 × 5 = 25 sq. cm.
Answer: 25 sq. cm
If the base of a parallelogram is doubled and its height remains the same, its area becomes:- a)Half
- b)Same
- c)Double
- d)Four Times
Correct answer is option 'C'. Can you explain this answer?
If the base of a parallelogram is doubled and its height remains the same, its area becomes:
a)
Half
b)
Same
c)
Double
d)
Four Times
| | Nidhi Bhatt answered |
Area = base × height
New area = (2 × base) × height = 2 × original area
New area = (2 × base) × height = 2 × original area
What is the area of a quadrilateral that can be divided into two triangles with areas of 20 sq. cm and 15 sq. cm?- a)40 sq. cm
- b)35 sq. cm
- c)30 sq. cm
- d)25 sq. cm
Correct answer is option 'B'. Can you explain this answer?
a)
40 sq. cm
b)
35 sq. cm
c)
30 sq. cm
d)
25 sq. cm
| | Nidhi Bhatt answered |
When a quadrilateral is partitioned into two non-overlapping triangles, its area equals the sum of the areas of the two triangles.
Area = 20 sq. cm + 15 sq. cm = 35 sq. cm.
Answer: 35 sq. cm
What unique property do the diagonals of a rhombus possess?- a)They divide the rhombus into rectangles
- b)They are parallel
- c)They are perpendicular bisectors of each other
- d)They are equal in length
Correct answer is option 'C'. Can you explain this answer?
What unique property do the diagonals of a rhombus possess?
a)
They divide the rhombus into rectangles
b)
They are parallel
c)
They are perpendicular bisectors of each other
d)
They are equal in length
| | Nidhi Bhatt answered |
The diagonals of a rhombus are perpendicular bisectors of each other, meaning they intersect at right angles and divide each other into equal segments. This unique property is essential for calculating the area of a rhombus accurately.
What happens to the area of triangles formed in a rectangle when both diagonals are drawn?- a)They become smaller
- b)Their areas depend on their angles
- c)They have equal areas
- d)They become larger
Correct answer is option 'C'. Can you explain this answer?
a)
They become smaller
b)
Their areas depend on their angles
c)
They have equal areas
d)
They become larger
| | Nidhi Bhatt answered |
Let the rectangle be ABCD and the diagonals AC and BD intersect at O.
In a rectangle (a parallelogram) the diagonals bisect each other; hence O is the midpoint of both AC and BD.
The diagonals divide the rectangle into four triangles whose total area equals the area of the rectangle. By symmetry and because opposite triangles are congruent, all four triangles have the same area.
Therefore, each triangle has equal area (each is one quarter of the rectangle's area).
If a triangle has a base of 8 units and the height from that base is 4 units, what is the area?- a)16 sq. units
- b)20 sq. units
- c)32 sq. units
- d)12 sq. units
Correct answer is option 'A'. Can you explain this answer?
a)
16 sq. units
b)
20 sq. units
c)
32 sq. units
d)
12 sq. units
| | Nidhi Bhatt answered |
Use the formula for the area of a triangle: Area = 1/2 × base × height.
Substitute base = 8 and height = 4: Area = 1/2 × 8 × 4.
Compute: 1/2 × 8 = 4, then 4 × 4 = 16.
Therefore, the area = 16 sq. units.
What is the area formula for a parallelogram?- a)Base - Height
- b)Base + Height
- c)½ × Base × Height
- d)Base × Height
Correct answer is option 'D'. Can you explain this answer?
a)
Base - Height
b)
Base + Height
c)
½ × Base × Height
d)
Base × Height
| | Nidhi Bhatt answered |
The area of a parallelogram is the product of its base and the corresponding height (the perpendicular distance between the parallel sides).
Area = Base × Height
In a rectangle, what is the relationship between the areas of the triangles formed by drawing a diagonal?- a)The triangles have equal areas
- b)The triangles have different areas
- c)The triangles have variable areas
- d)The triangles have no area
Correct answer is option 'A'. Can you explain this answer?
a)
The triangles have equal areas
b)
The triangles have different areas
c)
The triangles have variable areas
d)
The triangles have no area
| | Nidhi Bhatt answered |
Let the rectangle have length l and breadth b.
Area of the rectangle = l × b. A diagonal divides the rectangle into two congruent right-angled triangles, each occupying exactly half the rectangle.
Area of each triangle = 1/2 × l × b.
Therefore, the two triangles have equal areas.
If the height from base BC of triangle ABC is 3 units and the length of base BC is 5 units, what is the area of triangle ABC?- a)10 sq. units
- b)7.5 sq. units
- c)15 sq. units
- d)12 sq. units
Correct answer is option 'B'. Can you explain this answer?
If the height from base BC of triangle ABC is 3 units and the length of base BC is 5 units, what is the area of triangle ABC?
a)
10 sq. units
b)
7.5 sq. units
c)
15 sq. units
d)
12 sq. units
| | Nidhi Bhatt answered |
Area of a triangle = 1/2 × base × height.
Here base = 5 units and height = 3 units, so Area = 1/2 × 5 × 3.
Area = 1/2 × 15 = 7.5 sq. units.
Answer: 7.5 sq. units (Option B).
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