Question

In Fig. 29, ABCD is a quadrilateral in which diagonal AC = 84 cm; DL ⊥ AC, BM ⊥ AC, DL = 16.5 cm and BM = 12 cm. Find the area of quadrilateral ABCD.

Answer 1

We have,
AC = 84 cm, DL = 16.5 cm and BM = 12 cm
Area of Δ ADC = $$$\frac{1}{2}$x AC x DL
= $$$\frac{1}{2}$x 84 cm x 16.5 cm = 693 cm²
Area of Δ ABC = $$$\frac{1}{2}$x AC x BM
= $$$\frac{1}{2}$x 84 cm x 12 cm = 504 cm²
Hence,
Area of quadrilateral ABCD = Area of Δ ADC + Area of Δ ABC
= (693 + 504) cm²
= 1197 cm²