S K Gupta and Anubhuti Gangal Solutions for Chapter: Area of a Trapezium, a Polygon and Semicircle, Exercise 2: Exercise 21(A)

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.

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.

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.

$\mathrm{ABCD}$ is a trapezium of area $91 {\mathrm{cm}}^2$. $\mathrm{CD}$ is parallel to $\mathrm{AB}$ and $\mathrm{CD}$ is longer than $\mathrm{AB}$ by $8 \mathrm{cm}$. If the distance between $\mathrm{AB}$ and $\mathrm{CD}$ is $7 \mathrm{cm}$, find $\mathrm{AB}$ and $\mathrm{CD}$.

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 $₹ 4 \mathrm{per} {\mathrm{m}}^2$.

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.

In the figure, $AB$ and $DC$ are parallel sides of a trapezium $ABCD$ and $\angle ADC=90°$. Given, $\mathrm{AB}=15 \mathrm{cm},\mathrm{CD}=40 \mathrm{cm}$ and diagonal $AC=41 cm$, calculate the area of trapezium $\mathrm{ABCD}$

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