Question

find the area of the quadrilateral ABCD , in which AC = 36 cm. BL and DM perpendiculars from B and D to AC are 16 cm and 18 cm respectively .​

Answer 1

612 cm²

Explanation:

You want the area of quadrilateral ABCD with lengths AC = 36 cm, BL = 16 cm, and DM = 18 cm, where L and M are on AC and BL and DM are perpendicular to AC.

Triangles

The segment AC divides the quadrilateral into two triangles, each with base 36 cm. Segments BL and DM represent the heights of their respective triangles. The area is the sum of the areas of the two triangles.

A = 1/2(b·h1 +b·h2) = 1/2b(h1 +h2)

A = 1/2(36 cm)(16 cm +18 cm) = (18 cm)(34 cm) = 612 cm²

The area of quadrilateral ABCD is 612 cm².

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