M L Aggarwal Solutions for Chapter: Heron's Formula, Exercise 1: Exercise 12.1

Write whether the following statement is true or false. Justify your answer.

If the base and the corresponding altitude of a parallelogram are $10 \mathrm{cm}$ and  $3.5 \mathrm{cm}$ respectively, then the area of the parallelogram is $30 {\mathrm{cm}}^2$.

Write whether the following statement is true or false. Justify your answer.

If the side of a rhombus is $10 \mathrm{cm}$ and one diagonal is $16 \mathrm{cm}$ respectively, then the area of the rhombus is $96 {\mathrm{cm}}^2$.

Write whether the following statement is true or false. Justify your answer.

The area of a regular hexagon of side $\text{'}\mathrm{a}\text{'}$  is the sum of the areas of the five equilateral triangles with side $\mathrm{a}$. 

Find the area (in ${\mathrm{m}}^2$) of the trapezium $\mathrm{PQRS}$ with height $\mathrm{PQ}$ given in the adjoining figure.

The area of a trapezium is $475 {\mathrm{cm}}^2$ and the height is $19 \mathrm{cm}$. Find the lengths of its two parallel sides if one side is $4 \mathrm{cm}$ greater than the other.

A square and an equilateral triangles have equal perimeters. If a diagonal of the square is $24\sqrt{2} \mathrm{cm}$, then find the area of the triangle.

The base of an isosceles triangle is $4 \mathrm{cm}$ and its perimeter is $20 \mathrm{cm}$. Find the area of the triangle.

The perimeter of an isosceles triangle is $42 \mathrm{cm}$ and its base is $\frac{3}{2}$ times of each of its equal sides. Find the length of each side of the triangle, area of the triangle and the height corresponding to its longest side.