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
• B. 200
• C. 250
• D. 300

Answer 1

The correct option is C

250

We can calculate the area of this quadrilateral by considering it as the sum of two triangles.

Consider he diagonal AC of length 25m as the base for both triangles ($△ABCand△ADC$) 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 = $\frac{1}{2}\times 25\times 12$

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

Area of quadrilateral = $\frac{1}{2}\left(25\right)(8+12)=250m^2$