Question

The diagonal of a quadrilateral shaped field is 25m and the perpendiculars dropped on it from the remaining opposite vertices are 8m and 12m. Find the area of the field(in m²).

• A. 100 sq m
• B. 200 sq m
• C. 250 sq m
• D. 300 sq m

Answer 1

The correct option is C

250 sq m

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 = $\frac{1}{2}\times \text{base}\times \text{height}$
Area of the first triangle = $\frac{1}{2}\times 25\times 8$
Area of the second triangle = $\frac{1}{2}\times 25\times 12$
Area of quadrilateral = Area of the first triangle + Area of the second triangle = $\frac{1}{2}\left(25\right)(8+12)=250m^2$