M L Aggarwal Solutions for Chapter: Heron's Formula, Exercise 2: Exercise 12.2

Find the area of a triangle whose sides are $13 \mathrm{cm}$ and $14 \mathrm{cm}$ and its semi-perimeter is $18 \mathrm{cm}$. Give your answer to the nearest ${\mathrm{cm}}^2$ by rounding up to the nearest whole number. (use $\sqrt{10}=3.162$).

The perimeter of an isosceles triangle is $30 \mathrm{cm}$ and each of the equal sides measures $12 \mathrm{cm}$. Find the area of the triangle by using the Heron's formula.

Find the area of the triangular field of sides are $18 \mathrm{m}, 24 \mathrm{m}$and $30 \mathrm{m}$ by using Heron's formula. Also find its altitude corresponding to the shortest side.

The sides of a triangular plot are in the ratio $3:5:7$ and its perimeter is $300 \mathrm{m}$. Find its area.

There is a slide in a park. One of its side walls has been painted in some colour with a message "KEEP THE PARK GREEN AND CLEAN" (shown in the adjoining figure). If the sides of the wall are $15 \mathrm{m}, 11\mathrm{m}$ and $6 \mathrm{m}$, find the area painted in colour.

The triangular side walls of a flyover have been used for advertisement. The sides of the walls are $13 \mathrm{m}, 14 \mathrm{m}$ and $15 \mathrm{m}$. The advertisement yield an earning of $₹2000$ per ${\mathrm{m}}^2$ a year. A company hired one of its walls for  $6$ months. How much rent did it pay?

 A triangular park $\mathrm{ABC}$ has sides $120 \mathrm{m}, 80 \mathrm{m}$ and $50 \mathrm{m}$(as shown in the adjoining figure). A gardner Dhania has to put a fence around it and also plant grass inside. How much area does she need to plant? Find the cost of fencing it with barbed wire at the rate of $₹20$ per $\mathrm{meter}$ leaving a space $3 \mathrm{m}$ wide for a gate on one side.

In a rectangular field of dimensions $50 \mathrm{m}\times 30 \mathrm{m}$, a triangular park is constructed. If the side of the park are $15 \mathrm{m}, 14 \mathrm{m}$ and $13 \mathrm{m}$, find the area of the remaining field (in ${\mathrm{m}}^2$).