Question

A triangle and a trapezoid are equal in area. They also have the same altitude. If the base of the triangle is $18$ inches, the mean of the parallel sides of the trapezoid is __________.

• A. $36$ inches
• B. $9$ inches
• C. $18$ inches
• D. Can't be determined

Answer 1

The correct option is B $9$ inches

Let the altitude of both the Geometrical figure be $h$

As the Base of triangle is $18$

$\therefore$ Area of $△=\frac{1}{2}\times 18\times h$

Area of Trapezoid $=\frac{1}{2}\times \left(SumofparallelSide\right)\times h$

$\because$ Both the areas are equal by equating the area we get,

$⟹\frac{Sumofparallelside}{2}\times h=\frac{1}{2}\times 18\times h$

$⟹\frac{Sumofparallelside}{2}=9inches$