R. D. Sharma Solutions for Chapter: Heron's Formula, Exercise 2: EXERCISE

The area of the rhombus whose perimeter is $80 \mathrm{m}$ and one of whose diagonal is $24 \mathrm{m}$ is $k {\mathrm{m}}^2$. Find $k$.

Find the area of a quadrilateral $ABCD$ $\left(\mathrm{in} {\mathrm{cm}}^2\right)$ in which $AD=24 \mathrm{cm}, \angle BAD=90°$ and $BCD$ forms an equilateral triangle whose each side is equal to $26 \mathrm{cm}$. (Take $\sqrt{3}=1.73$ )

Find the area of a quadrilateral $ABCD$ $\left(\mathrm{in} {\mathrm{cm}}^2\right)$ in which $AB=42 \mathrm{cm}, BC=21 \mathrm{cm}, CD=29 \mathrm{cm}, DA=34 \mathrm{cm}$ and diagonal $BD=20 \mathrm{cm}$.

The adjacent sides of a parallelogram $ABCD$ measure $34 \mathrm{cm}$ and $20 \mathrm{cm}$, and the diagonal $AC$ measures $42 \mathrm{cm}$. The area of the parallelogram$=$_____${\mathrm{cm}}^2$.

Find the area of the blades $\left(\mathrm{in} {\mathrm{cm}}^2\right)$ of the magnetic compass shown in Figure (Take $\sqrt{11}=3.32$)

A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are $13 \mathrm{cm},14 \mathrm{cm}$ and $15 \mathrm{cm}$ and the parallelogram stands on the base $14 \mathrm{cm}$, find the height of the parallelogram.

Two parallel side of a trapezium are $60 \mathrm{cm}$ and $77 \mathrm{cm}$ and other sides are $25 \mathrm{cm}$ and $26 \mathrm{cm}$. The area of the trapezium$=$_____${\mathrm{cm}}^2$.

A hand fan is made by stitching $10$ equal size triangular strips of two different types of paper as shown in figure. The dimensions of equal strips are $25 \mathrm{cm}, 25 \mathrm{cm}$ and $14 \mathrm{cm}$. The area of each type of paper needed to make the hand fan$=$_____${\mathrm{cm}}^2$.