# Find the area of a quadrilateral whose diagonal length is $10cm$, height ${h_1} = 5cm$ and height ${h_2} = 7cm$ .

Last updated date: 27th Mar 2023

•

Total views: 206.4k

•

Views today: 4.83k

Answer

Verified

206.4k+ views

**Hint:**In this problem we need to find area of quadrilateral, since they have given height of triangle as $5cm$ and $7cm$ we can find the area of triangle individually and add the area of triangle to get the area of quadrilateral.

**Complete step-by-step solution:**

Let us consider a quadrilateral $ABCD$ as shown below.

Let ${h_1}$ be the height of triangle $ABC$ and ${h_2}$ be the height of the triangle $BDC$

Given:

$BC = 10cm$

${h_1} = 5cm$ and ${h_2} = 7cm$

We know that, area of quadrilateral = area of triangle $ABC$ $ + $ area of triangle $BCD$

And also, area of triangle $ = \dfrac{1}{2} \times base \times height$

Therefore, area of quadrilateral $ = \dfrac{1}{2} \times BC \times {h_1} + \dfrac{1}{2} \times BC \times {h_2}$

Substituting the given data in above equation we get,

$ = \left( {\dfrac{1}{2} \times 10 \times 5 + \dfrac{1}{2} \times 10 \times 7} \right)c{m^2}$

On simplifying,

$ = \left( {25 + 35} \right)c{m^2}$

Therefore,

**Area of quadrilateral $ABCD$ $ = 60c{m^2}$.**

**Note:**The quadrilateral is the combination of the basic geometric shapes which includes two triangles. Two calculate the area of a quadrilateral, the area of two individual triangles should be computed and the area of the individual triangle should be added. The quadrilateral is the closed, two dimensional figure which has four sides.

Recently Updated Pages

If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE