Sanya has a piece of land which is in the sha | vedclass

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

Question

(A) Let $ABCD$ be the rhombus-shaped field.Perimeter of the rhombus $= 400\, m$.Since all sides of a rhombus are equal,each side $= 400\, m / 4 = 100\

Vedclass · Accepted Answer

$4800$

Vedclass · Answer

(A) Let $ABCD$ be the rhombus-shaped field.Perimeter of the rhombus $= 400\, m$.Since all sides of a rhombus are equal,each side $= 400\, m / 4 = 100\, m$.Thus,$AB = BC = CD = DA = 100\, m$.Let the diagonal $BD = 160\, m$.The diagonal divides the rhombus into two congruent triangles,$	riangle ABD$ and $	riangle BCD$.For $	riangle ABD$,the sides are $a = 100\, m$,$b = 100\, m$,and $c = 160\, m$.The semi-perimeter $s$ is given by:$s = (100 + 100 + 160) / 2 = 360 / 2 = 180\, m$.Using Heron's formula,the area of $	riangle ABD$ is:Area $= \sqrt{s(s-a)(s-b)(s-c)}$Area $= \sqrt{180(180-100)(180-100)(180-160)}$Area $= \sqrt{180 	imes 80 	imes 80 	imes 20}$Area $= \sqrt{180 	imes 20 	imes 80^2}$Area $= \sqrt{3600 	imes 6400}$Area $= 60 	imes 80 = 4800\, m^2$.Since the land is divided into two equal parts,each of them will get an area of $4800\, m^2$.

Similar Questions

The sides of a triangle measure $12 \, cm$,$16 \, cm$,and $20 \, cm$. What is the area of the triangle in $cm^2$?

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?

Find the area of a triangle whose sides are $33 \, cm$,$34 \, cm$,and $65 \, cm$. (in $, cm^2$)

Find the area of a triangle,two sides of which are $15\,cm$ and $28\,cm$ and the perimeter is $84\,cm$. (in $,cm^2$)

An isosceles triangle has a perimeter of $50\,cm$ and each of the equal sides is $17\,cm$. Find the area of the triangle. (in $,cm^2$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module