Question

Calculate the area of the quadrilateral ABCD as shown in Fig. 33, given that BD = 42 cm, AC = 28 cm, OD = 12 cm and AC ⊥ BD.

Answer 1

We have,
BD = 42 cm, AC = 28 cm, OD = 12 cm
Area of ΔABC = $\frac{1}{2}$ x AC x OB
= $\frac{1}{2}$ x AC x (BD − OD)
= $\frac{1}{2}$ x 28 cm x (42 cm − 12 cm) = $\frac{1}{2}$ x 28 cm x 30 cm = 14 cm x 30 cm = 420 cm²
Area of Δ ADC = $\frac{1}{2}$ x AC x OD
= $\frac{1}{2}$ x 28 cm x 12 cm = 14 cm x 12 cm = 168 cm²
Hence,
Area of the quadrilateral ABCD = Area of Δ ABC + Area of Δ ADC

= (420 + 168) cm² = 588 cm²