M L Aggarwal Solutions for Chapter: Heron's Formula, Exercise 3: Exercise 12.3

A field in the form of a parallelogram has sides $60 \mathrm{m}, 40 \mathrm{m}$ and one of its diagonal is $80 \mathrm{m}$ long. Find the area of the parallelogram.

If the perimeter of a rhombus is $400 \mathrm{m}$ and its one diagonal is $160 \mathrm{m}$ long, find the area of the rhombus (in ${\mathrm{m}}^2$).

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

The sides of a quadrilateral $\mathrm{ABCD}$ are $6 \mathrm{cm}, 8 \mathrm{cm}, 12 \mathrm{cm}$ and $14 \mathrm{cm}$ (taken in order) respectively and the angle between the first two sides is a right angle. Find its area.

Two parallel sides of a trapezium are $60 \mathrm{cm}$ and $77 \mathrm{cm}$ and the other two sides are $25 \mathrm{cm}$ and $26 \mathrm{cm}$. Find the area of the trapezium.

In the given figure, $△\mathrm{ABC}$ has sides $\mathrm{AB}=7.5 \mathrm{cm}, \mathrm{AC}=6.5 \mathrm{cm}$ and $\mathrm{BC}=7 \mathrm{cm}$. On the base $\mathrm{BC}$, a parallelogram $\mathrm{DBCE}$ of same area as that of $△\mathrm{ABC}$ is constructed. Find the height $\mathrm{DF}$ of the parallelogram (in $\mathrm{cm}$).

A floral design on a floor is made up of $16$ tiles which are triangular, the sides of the triangle being $9 \mathrm{cm}, 28 \mathrm{cm}$ and $35 \mathrm{cm}$ as shown in the given figure. Find the cost of polishing the tiles, at the rate of $50$ paise per ${\mathrm{cm}}^2$.

An umbrella is made by stitching $10$ triangular pieces of cloth of two different colours as shown in the given figure, each piece measuring $20 \mathrm{cm}, 50 \mathrm{cm}$ and $50 \mathrm{cm}$. How much cloth of each colour is required for the umbrella?