Areas of Parallelograms and Triangles - Exercise 14.3 | Extra Documents & Tests for Class 9 PDF Download

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Question:6
In the given figure, compute the area of quadrilateral ABCD.
 
Solution:
Given: Here from the given figure we get
1 ABCD is a quadrilateral with base AB,
2 ?ABD is a right angled triangle
3 ?BCD is a right angled triangle with base BC right angled at B
To Find: Area of quadrilateral ABCD
Calculation:
In right triangle ?BCD, by using Pythagoreans theorem
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Question:6
In the given figure, compute the area of quadrilateral ABCD.
 
Solution:
Given: Here from the given figure we get
1 ABCD is a quadrilateral with base AB,
2 ?ABD is a right angled triangle
3 ?BCD is a right angled triangle with base BC right angled at B
To Find: Area of quadrilateral ABCD
Calculation:
In right triangle ?BCD, by using Pythagoreans theorem
 
.So
In right triangle ABD
Hence we get Area of quadrilateral ABCD =
Question:7
In the given figure, PQRS is a square and T and U are, respectively, the mid-points of PS and QR. Find the area of ?
OTS if PQ = 8 cm.
Solution:
Given: Here from the given figure we get
1 PQRS is a square,
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Question:6
In the given figure, compute the area of quadrilateral ABCD.
 
Solution:
Given: Here from the given figure we get
1 ABCD is a quadrilateral with base AB,
2 ?ABD is a right angled triangle
3 ?BCD is a right angled triangle with base BC right angled at B
To Find: Area of quadrilateral ABCD
Calculation:
In right triangle ?BCD, by using Pythagoreans theorem
 
.So
In right triangle ABD
Hence we get Area of quadrilateral ABCD =
Question:7
In the given figure, PQRS is a square and T and U are, respectively, the mid-points of PS and QR. Find the area of ?
OTS if PQ = 8 cm.
Solution:
Given: Here from the given figure we get
1 PQRS is a square,
2 T is the midpoint of PS which means 
3 U is the midpoint of PS which means 
4 QU = 8 cm
To find: Area of ?OTS
Calculation:
Since it is given that PQ = 8 cm. So
Since T and U are the mid points of PS and QR respectively. So
Therefore area of triangle OTS is equals to
Hence we get the result that Area of triangle OTS is
 
Question:8
Compute the area of trapezium PQRS in the given figure.
Solution:
Given:
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Question:6
In the given figure, compute the area of quadrilateral ABCD.
 
Solution:
Given: Here from the given figure we get
1 ABCD is a quadrilateral with base AB,
2 ?ABD is a right angled triangle
3 ?BCD is a right angled triangle with base BC right angled at B
To Find: Area of quadrilateral ABCD
Calculation:
In right triangle ?BCD, by using Pythagoreans theorem
 
.So
In right triangle ABD
Hence we get Area of quadrilateral ABCD =
Question:7
In the given figure, PQRS is a square and T and U are, respectively, the mid-points of PS and QR. Find the area of ?
OTS if PQ = 8 cm.
Solution:
Given: Here from the given figure we get
1 PQRS is a square,
2 T is the midpoint of PS which means 
3 U is the midpoint of PS which means 
4 QU = 8 cm
To find: Area of ?OTS
Calculation:
Since it is given that PQ = 8 cm. So
Since T and U are the mid points of PS and QR respectively. So
Therefore area of triangle OTS is equals to
Hence we get the result that Area of triangle OTS is
 
Question:8
Compute the area of trapezium PQRS in the given figure.
Solution:
Given:
1 PQRS is a trapezium in which SR||PQ..
2 PT = 5 cm.
3 QT = 8 cm.
4 RQ = 17 cm.
To Calculate: Area of trapezium PQRS.
Calculation:
In triangle
.So
No area of rectangle PTRS
Therefore area of trapezium PQRS is
Hence the answer is
Question:9
In the given figure, ?AOB = 90°, AC = BC, OA = 12 cm and OC = 6.5 cm. Find the area of ? AOB.
Solution:
Given: In figure:
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Question:6
In the given figure, compute the area of quadrilateral ABCD.
 
Solution:
Given: Here from the given figure we get
1 ABCD is a quadrilateral with base AB,
2 ?ABD is a right angled triangle
3 ?BCD is a right angled triangle with base BC right angled at B
To Find: Area of quadrilateral ABCD
Calculation:
In right triangle ?BCD, by using Pythagoreans theorem
 
.So
In right triangle ABD
Hence we get Area of quadrilateral ABCD =
Question:7
In the given figure, PQRS is a square and T and U are, respectively, the mid-points of PS and QR. Find the area of ?
OTS if PQ = 8 cm.
Solution:
Given: Here from the given figure we get
1 PQRS is a square,
2 T is the midpoint of PS which means 
3 U is the midpoint of PS which means 
4 QU = 8 cm
To find: Area of ?OTS
Calculation:
Since it is given that PQ = 8 cm. So
Since T and U are the mid points of PS and QR respectively. So
Therefore area of triangle OTS is equals to
Hence we get the result that Area of triangle OTS is
 
Question:8
Compute the area of trapezium PQRS in the given figure.
Solution:
Given:
1 PQRS is a trapezium in which SR||PQ..
2 PT = 5 cm.
3 QT = 8 cm.
4 RQ = 17 cm.
To Calculate: Area of trapezium PQRS.
Calculation:
In triangle
.So
No area of rectangle PTRS
Therefore area of trapezium PQRS is
Hence the answer is
Question:9
In the given figure, ?AOB = 90°, AC = BC, OA = 12 cm and OC = 6.5 cm. Find the area of ? AOB.
Solution:
Given: In figure:
1
?AOB = 90°
2 AC = BC,
3 OA = 012 cm,
4 OC = 6.5 cm.
To find: Area of ?AOB
Calculation:
It is given that AC = BC where C is the mid point of AB
We know that the mid point of hypotenuse of right triangle is equidistant from the vertices
Therefore
CA = BC = OC
? CA = BC = 6.5
? AB = 2 × 6.5 = 13 cm
Now inn triangle OAB use Pythagoras Theorem
So area of triangle OAB
Hence area of triangle is
 
Question:10
In the given figure, ABCD is a trapezium in which AB = 7 cm, AD = BC = 5 cm, DC = x cm, and distance between AB
and DC is 4 cm. Find the value of x and area of trapezium ABCD.