Question

In the adjoining figure, ABCD is a quadrilateral in which diag. BD = 14cm. If AL ⊥ BD and CM ⊥ BD such that AL = 8cm and CM = 6cm, find the area of quad. ABCD.

Answer 1

We know that

Area of △ BAD = ½ × BD × AL

By substituting the values in the above equation

Area of △ BAD = ½ × 14 × 8

By multiplication

Area of △ BAD = 56 cm²

We know that

Area of △ CBD = ½ × BD × CM

By substituting the values in the above equation

Area of △ CBD = ½ × 14 × 6

By multiplication

Area of △ CBD = 42 cm²

So we get

Area of quadrilateral ABCD = Area of △ ABD + Area of △ CBD

By substituting the values

Area of quadrilateral ABCD = 56 + 42

By addition

Area of quadrilateral ABCD = 98 cm²

Therefore, area of quadrilateral ABCD is 98 cm².