Question

If AB= 14cm ,BC= 13cm CD= 17cm DA = 8cm and AC= 15CM .Then the area of quadrilateral ABCD is A.150cm2 B.144cm2 C. 142cm2 D. 140cm2

Answer 1

Question :

If AB= 14cm ,BC= 13cm CD= 17cm DA = 8cm and AC= 15cm.Then the area of quadrilateral ABCD is

A. 159cm²

B. 144cm²

C. 142cm²

D. 140cm²

Solution :

▪️Area of Quadrilateral = Area of ∆ABC + Area of ∆ADC.

▪️Area of Quadrilateral = 1/2 × base × height + 1/2 × base × height

or 1/2 × base × ( sum of perpendicular sides)

By using the 1st formulae,

Area of Quadrilateral = 1/2 × base × height + 1/2 × base × height

Area of Quadrilateral = 1/2 × 17cm× 8cm + 1/2 × 13cm× 14cm

= 17cm × 4cm + 13cm × 7cm

= 68cm² + 91cm²

= 159cm²

Thus, area of quadrilateral is 159cm²(option A.).