Question

The diagonal of a quadrilateral shaped field is 25m and the perpendiculars dropped on it from the remaining opposite vertices are 8m and 14m. Find the area of the field(in m²).

• A. 100 square metres
• B. 200 square metres
• C. 275 square metres
• D. 300 square metres

Answer 1

The correct option is C

275 square metres

We can calculate the area of this quadrilateral as the sum of two triangles taking diagonal length 25m as the base for both triangles and perpendicular length 8m as a height of one triangle and perpendicular length 12m as a height of another triangle.

Area of triangle = $\frac{1}{2}\times base\times height$

Area of the first triangle = $\frac{1}{2}\times 25\times 8$

Area of the second triangle = $\frac{1}{2}\times 25\times 14$

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

Area of quadrilateral = $\frac{1}{2}\left(25\right)(8+14)=275m^2$