S.chand Class 8 Maths Solution Chapter 16 Area of a Trapezium and a Polygon Exercise 16 A

 Exercise 16 A

Question 1

Find the area of the following trapeziums :

	Height	Parallel sides		Height	Parallel sides
(a)	7 cm	8 cm and 10 cm	(b)	15 cm	10 cm and 12 cm
(b)	2 cm	2.2 cm and 3.5 cm	(d)	4 cm	15 cm and 7.8 cm

2. A garden is in the form of a trapezium whose parallel sides are $40 \mathrm{~m}$ and $22 \mathrm{~m}$ and the perpendicular distance between them is $12 \mathrm{~m}$. Find the area of the garden.

3. Two parallel sides of a trapezium are $85 \mathrm{~cm}$ and $63 \mathrm{~cm}$ and its area is $2664 \mathrm{~cm}^{2}$. Find its altitude.

4. Find the height of the trapezium, the sum of the lengths of whose bases is $50 \mathrm{~cm}$, and whose area is $500 \mathrm{~cm}^{2}$

5. Find the sum of the lengths of the bases of a trapezium whose altitude is $17 \mathrm{~cm}$ and whose area is $0.85 \mathrm{~m}^{2}$.

6. The area of a trapezium is $210 \mathrm{~cm}^{2}$ and its height is $14 \mathrm{~cm}$. If one of the parallel sides is double that of the other, find the two parallel sides.

7. The area of a trapezium is $300 \mathrm{~m}^{2}$. The perpendicular distance between the two parallel sides is $15 \mathrm{~m}$. If the difference of the parallel sides is $16 \mathrm{~m}$, find the length of the parallel sides.

8. The lengths of the parallel sides of a trapezium are in the ratio $3: 5$ and the distance between them is $10 \mathrm{~cm}$. If the area of trapezium is $120 \mathrm{~cm}^{2}$, find the lengths of its parallel sides.

9. Two parallel sides of an isosceles trapezium are $6 \mathrm{~cm}$ and $14 \mathrm{~cm}$ respectively. If the length of each non-parallel side is $5 \mathrm{~cm}$, find the area of the trapezium.

10. $A B C D$ is a trapezium of area $91 \mathrm{~cm}^{2} . C D$ is parallel to $A B$ and $C D$ is longer than $A B$ by $8 \mathrm{~cm}$. If the distance between $A B$ and $C D$ is $7 \mathrm{~cm}$, find $A B$ and $C D$.

11. Find the cost of watering a trapezoidal field whose parallel sides are $10 \mathrm{~m}$ and $25 \mathrm{~m}$ respectively, the perpendicular distance between them is $15 \mathrm{~m}$ and the rate of watering is $₹ 4$ per $\mathrm{m}^{2}$.

12. The parallel sides of a trapezium are $25 \mathrm{~cm}$ and $13 \mathrm{~cm}$, its non-parallel sides are equal, each being $10 \mathrm{~cm}$. Find the area of the trapezium.

13. In the figure, $A B$ and $D C$ are parallel sides of a trapezium $A B C D$ and $\angle A D C=90^{\circ}$. Given $A B=15 \mathrm{~cm}, C D=40 \mathrm{~cm}$ and diagonal $A C=41 \mathrm{~cm}$, calculate the area of trapezium $A B C D$.

[Hint. In $\triangle A D C, A D=\sqrt{A C^{2}-D C^{2}}=\sqrt{41^{2}-40^{2}}=9 \mathrm{~cm}$ Now, Area of trap, $\left.A B C D=\frac{1}{2} \times A D \times(A B+D C)\right]$

14. Find the area of the pentagonal field shown alongside. All dimensions are in metres.