Question

The diagonal of a quadrilateral is 20cm and the length of the perpendiculars to it from the

opposite vertices are 6cm and 4cm . Find the area of the quadrilateral.​

Answer 1

★Given :

• Length of diagonal = 20cm
• Length of perpendiculars to it from the  opposite vertices are 6cm and 4cm .

★To find :

• Area of the quadrilateral.

★Solution :

$\setlength{\unitlength}{1.2 cm}\begin{picture}(0,0)\linethickness{0.4mm}\qbezier(0,0)(0,0)(1,3)\qbezier(4.6,1)(4.6,1)(4,3)\qbezier(1,3)(1,3)(4,3)\qbezier(4.6,1)(4.6,1)(0,0)\qbezier(4,3)(4,3)(0,0)\qbezier(4.6,1)(4.6,1)(3,2.25)\qbezier(2,1.5)(2,1.5)(1,3)\qbezier(2.2,1.7)(2.2,1.7)(2.05,1.9)\qbezier(2.05,1.9)(2.05,1.9)(1.82,1.74)\qbezier(3.25,2.4)(3.25,2.4)(3.44,2.25)\qbezier(3.44,2.25)(3.44,2.25)(3.25,2.05)\put(-0.4,-0.5){\sf C}\put(4.8,0.6){\sf B}\put(4.2,3.2){\sf A}\put(0.4,3){\sf D}\end{picture}$

We are given the diagonal and the length of the perpendiculars from the vertices, the area of the quadrilateral is calculated using the formula :

$\leadsto \underline{\boxed{\sf Area = \dfrac{1}{2}\times length\ of\ diagonal \times (sum\ of\ perpendicular's) }}$

Sum of perpendicular's :

→6 + 4

→10 cm

Substituting values in the formula,

$\implies \sf Area = \dfrac{1}{2} \times 20 \times 10 \\\\\implies \sf Area = 10 \times 10 \\\\\implies \underline{\boxed{\bold{Area = 100cm^2.}}}$

∴The area of the quadrilateral is 100cm².

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