Question

find the area of the quadrilateral

Answer 1

Answer:

If the diagonal and the length of the perpendiculars from the vertices are given, then the area of the quadrilateral is calculated as: Area of quadrilateral = (½) × diagonal length × sum of the length of the perpendiculars drawn from the remaining two vertices

Step-by-step explanation:

Answer 2

Answer:

114 cm²

Step-by-step explanation:

Dividing answer into 2 parts:

(1) A(ΔSPQ)

(2) Find SQ

(3) A(ΔSQR)

(4) A(ΔSPQ)+A(ΔSQR)

(1)

A(ΔSPQ) = 1/2 × b × h

= 1/2 × 12 × 9

A(ΔSPQ) = 54 cm²

(2)

In ΔSPQ , ∠P=90°

By Pythagoras theorem,

SQ²=SP²+PQ²

= 9²+12²

= 81+144

= 225

SQ = 15 cm

(3)

A(ΔSQR) = 1/2 × b × h

= 1/2 × 8 × 15

A(ΔSQR) = 60 cm²

(4)

A(ΔSPQ)+A(ΔSQR) = 54cm²+60cm²

= 114 cm²