Question

A quadrilateral has an area of $453.6m^2$. The length of a diagonal is 42 m and the perpendicular distance from one vertex to the diagonal is 10 m. What is the perpendicular distance from the other vertex to the diagonal ?

• A. 23.2 m
• B. 11.6 m
• C. 11 m
• D. 22 m

Answer 1

The correct option is B

11.6 m

Area of a quadrilateral can be written as the sum of areas of two triangles.

Let the perpendicular distance from the other vertex be $x$.

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

Area of the quadrilateral $=\frac{1}{2}\times 42\times 10+\frac{1}{2}\times 42\times x$

$453.6=\frac{1}{2}\times 42(10+x)$

$x=11.6m$.