Question

A diagonal of a quadrilateral is 20m in length and the perpendiculars to it from the opposite vertices are 7:5m and 9:5m . find the area of the quadrilateral.​

Answer 1

Topic

Area

Given

A diagonal of a quadrilateral is 20m in length and the perpendiculars to it from the opposite vertices are 7.5m and 9.5m.

To Find

The area of quadrilateral.

Concept

A diagonal of a quadrilateral divides it into two triangles.

Formula

Area of Triangle = 1/2 × Base × Height

Solving

We can see that quadrilateral is divided into two triangles by diagonal which means Sum of area of both of the triangles will be area of Quadrilateral.

Area of Triangle ABD,

1/2 × 20 m × 7.5 m = 75 m²

Area of Triangle BCD,

1/2 × 20 m × 9.5 m = 95 m²

Note :- Base is common for both triangles.

Area of Quadrilateral =

Area of Triangle ABD + Area of Triangle BCD

ar( ABCD ) = ar( ∆ABD ) + ar ( ∆BCD )

ar( ABCD ) = 75 m² + 95 m²

ar( ABCD ) = 170 m²

Answer

So, the area of the Quadrilateral is 170m²