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Question

The diagonal of a quadrilateral shaped field is 24m and the perpendiculars dropped on it from the remaining opposite vertices are 8m and 12m. Find the area of the field(in m2).

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Solution

We can calculate the area of this quadrilateral as the sum of two triangles taking diagonal length 24m as the base for both triangles and perpendicular length 8m as the height of one triangle and perpendicular length 12m as the height of the other triangle.

Area of triangle = 12×base×height

Area of the first triangle = 12×24×8

Area of the second triangle = 12×24×12

Area of quadrilateral = Area of the first triangle + Area of the second triangle

Area of quadrilateral = 12(24)(8+12)=240m2

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