Question

In the quadrilateral ABCD, ∠BAD = 90° and ∠BDC = 90°, All measurements are in centimetres. Find the area of the quadrilateral ABCD, where AB = 6 cm, AD = 8 cm and BC = 26 cm.

Answer 1

According to Pythagoras theorem, BD2 = AB2 + AD2

⇒ BD2 = 62 + 82
⇒ BD2 = 36 + 64
⇒ BD2 = 100
⇒ BD = 10 cm

Area of triangle ABD = 1/2 × base × height
= 1/2 × AB × AD
= 1/2 × 6 × 8
= 24 sq cm

According to Pythagoras theorem, BC2 = BD2 + CD2

⇒ 262 = 102 + CD2
⇒ CD2 = 676 - 100
⇒ CD2 = 576
⇒ BD = 24 cm

Area of triangle BDC = 1/2 × base × height
= 1/2 × BD × CD
= 1/2 × 10 × 24
= 120 sq cm

Area of the quadrilateral ABCD = Area of triangle ABD + Area of triangle BDC
= 24 + 120
= 144 sq cm.

Answer 2

Area of the quadrilateral ABCD is 144cm^2.