Question

Find the area of a quadrilateral ABCD which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm, and AC = 5 cm.

Answer 1

In quadrilateral ABCD, AC is the diagonal. 

In ∆ABC, a = 5cm, b = 3 cm, c = 4 cm. 

∴ Perimeter = a + b + c = 5 + 3 + 4 = 12 cm.

∴ Area(∆ABC) = 6 sq. cm. 

In ∆ADC, a₁ = 5cm, b₁ = 5 cm, c₁ = 4cm. 

∴ Perimeter = a₁ + b₁ + c₁ 

= 5 + 5 + 4 = 14 cm.

Area of ∆ADC = 9.16 sq.cm. 

∴ Area of quadrilateral aBCD, 

= Area(∆ABC) + Area(∆ADC) 

= 6 + 9.16 

= 15.16 sq. cm.