Monica Capoor Solutions for Chapter: Mensuration I Area of Polygons, Exercise 3: EXERCISE

The area of a trapezium is $660 {\mathrm{cm}}^2$ and the length of one of the parallel sides is $28 \mathrm{cm}$. If the height is $30 \mathrm{cm}$, find the length of the other parallel side.

The area of a trapezium is $120 {\mathrm{cm}}^2$ and the distance between its parallel sides is $8 \mathrm{cm}$. Find the length of the parallel sides if their difference is $6 \mathrm{cm}$.

The area of a trapezium is $180 {\mathrm{cm}}^2$. Its parallel sides are in ratio $1:2$ and the distance between them is $12 \mathrm{cm}$. Find the length of each of the parallel sides.

In figure, a parallelogram is drawn in a trapezium. The area of the parallelogram is $390 {\mathrm{cm}}^2$. If the area of the trapezium is $k {\mathrm{cm}}^2$, find the value of $k$.

In figure, $\mathrm{AB}\parallel \mathrm{DC}$ and $\mathrm{DA}\perp \mathrm{AB}$. If $\mathrm{DC}=7 \mathrm{cm}, \mathrm{CB}=10 \mathrm{cm}$ and $\mathrm{AB}=13 \mathrm{cm}$. The area of the quadrilateral $\mathrm{ABCD}$ is $k {\mathrm{cm}}^2$. Find $k$.

A field is in the shape of a trapezium. Its parallel sides are $40 \mathrm{m}$ and $83 \mathrm{m}$ and the distance between them is $38 \mathrm{m}$. If the cost of ploughing the field at the rate of $₹10 \mathrm{per} {\mathrm{m}}^2$ is $k {\mathrm{m}}^2$, find the value of $k$.

The parallel sides of a trapezium are $12 \mathrm{cm}$ and $36 \mathrm{cm}$. Its non-parallel sides are equal each being $15 \mathrm{cm}$. The area of the trapezium is $k {\mathrm{cm}}^2$. Find $k$.

The area of a trapezium is $0.05 {\mathrm{m}}^2$ and its height is $20 \mathrm{cm}$. If one of the parallel side is longer than the other by $8 \mathrm{cm}$. The length of the longer parallel side is $k \mathrm{cm}$. Find $k$.