Find the area of a triangle,two sides of whic | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given,the perimeter of the triangle is $32 \, cm$. Let the sides be $a = 8 \, cm$ and $b = 11 \, cm$.The third side $c$ is calculated as:$c = 32 \

Vedclass · Accepted Answer

$8 \sqrt{30} \, cm^2$

Vedclass · Answer

(A) Given,the perimeter of the triangle is $32 \, cm$. Let the sides be $a = 8 \, cm$ and $b = 11 \, cm$.The third side $c$ is calculated as:$c = 32 \, cm - (8 + 11) \, cm = 32 \, cm - 19 \, cm = 13 \, cm$.The semi-perimeter $s$ is:$s = \frac{	ext{Perimeter}}{2} = \frac{32}{2} \, cm = 16 \, cm$.Now,calculate $(s - a)$,$(s - b)$,and $(s - c)$:$s - a = 16 - 8 = 8 \, cm$$s - b = 16 - 11 = 5 \, cm$$s - c = 16 - 13 = 3 \, cm$Using Heron's formula,the area of the triangle is:$	ext{Area} = \sqrt{s(s - a)(s - b)(s - c)}$$	ext{Area} = \sqrt{16 	imes 8 	imes 5 	imes 3} \, cm^2$$	ext{Area} = \sqrt{16 	imes 120} \, cm^2$$	ext{Area} = 4 	imes \sqrt{4 	imes 30} \, cm^2$$	ext{Area} = 4 	imes 2 \sqrt{30} \, cm^2 = 8 \sqrt{30} \, cm^2$.

Find the area of a triangle,two sides of which are $8 \, cm$ and $11 \, cm$ and the perimeter is $32 \, cm$.

Similar Questions

Radha made a picture of an aeroplane with coloured paper as shown in the figure. Find the total area of the paper used. (in $, cm^{2}$)

Sides of a triangle are in the ratio of $12 : 17 : 25$ and its perimeter is $540 \, cm$. Find its area.

The triangular side walls of a flyover have been used for advertisements. The sides of the walls are $122\, m, 22\, m$ and $120\, m$ (see Fig.). The advertisements yield an earning of $Rs. 5000$ per $m^2$ per year. $A$ company hired one of its walls for $3$ months. How much rent did it pay?

$A$ floral design on a floor is made up of $16$ tiles which are triangular,the sides of the triangle being $9\, cm, 28\, cm$ and $35\, cm$ (see Fig.). Find the cost of polishing the tiles at the rate of $50p$ per $cm^2$.

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module