A diagonal of a quadrilateral is 26 cm and the perpendiculars drawn to it from the opposite vertices are 12.8 cm and 11.2 cm. Find the area of the quadrilateral.

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Solution

We have:
AC = 26 cm, DL = 12.8 cm and BM = 11.2 cm

Area of ΔADC = $\frac{1}{2}$ $\times$ AC $\times$ DL
= $\frac{1}{2}$ $\times$ 26 cm $\times$ 12.8 cm = 166.4 cm²
Area of ΔABC = $\frac{1}{2}$ $\times$ AC $\times$ BM
= $\frac{1}{2}$ $\times$ 26 cm $\times$ 11.2 cm = 145.6 cm²

∴ Area of the quadrilateral ABCD = Area of ΔADC + Area of ΔABC
= (166.4 + 145.6) cm²
= 312 cm²

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A diagonal of a quadrilateral is 26 cm and the perpendiculars drawn to it from the opposite vertices are 12.8 cm and 11.2 cm. Find the area of the quadrilateral.

We have: AC = 26 cm, DL = 12.8 cm and BM = 11.2 cm Area of ΔADC = 12 × AC × DL = 12 × 26 cm × 12.8 cm = 166.4 cm2 Area of ΔABC = 12 × AC × BM = 12 × 26 cm × 11.2 cm = 145.6 cm2 ∴ Area of the quadrilateral ABCD = Area of ΔADC + Area of ΔABC = (166.4 + 145.6) cm2 = 312 cm2