Question

A tabletop in the shape of a trapezoid has an area of 6,664 square centimeters. Its longer base measures119 centimeters, and the shorter base is 105 centimeters. What is the height?The height of the tabletop is centimeters.

Answer 1

The area of a trapezoid (A) is:

$A=\frac{1}{2}\cdot(a+b)\cdot h$

Where:

a and b are the bases of the trapezoid.

h is the height.

In this question:

a = 119 cm

b = 105 cm

A = 6,664 square cm

Substituting the values in the equation:

$6,664=\frac{1}{2}\cdot(119+105)\cdot h$

Solving the equation:

$\begin{gathered} 6,664=\frac{1}{2}\cdot(224)\cdot h \\ 6,664=112\cdot h \end{gathered}$

Dividing both sides by 112:

$\begin{gathered} \frac{6,664}{112}=\frac{112}{112}\cdot h \\ 59.5=h \end{gathered}$

Answer: The height of the tabletop is 59.5 centimeters.