Question

The total area of a polygon is 176 sq.ft. Find the value of x in the drawing

Answer 1

Answer:

x=6 ft

Explanation:

The given polygon is a trapezium in which:

• The parallel sides are a=16 ft and b=(16+2x) ft

,

• The height, h = 8 ft

,

• Area = 176 sq.ft.

The area of a trapezium is calculated using the formula:

$\begin{gathered} A=\frac{1}{2}(a+b)h \\ a,b\text{ are the parallel sides} \\ h\text{ is the perpendicular height} \end{gathered}$

Substitute all the known values:

$\begin{gathered} 176=\frac{1}{2}\times8(16+16+2x) \\ 176=4(32+2x) \end{gathered}$

Divide both sides by 4.

$\begin{gathered} \frac{176}{4}=32+2x \\ 44=32+2x \end{gathered}$

Subtract 32 from both sides:

$\begin{gathered} 44-32=32-32+2x \\ 12=2x \end{gathered}$

Divide both sides by 2.

$\begin{gathered} \frac{12}{2}=\frac{2x}{2} \\ x=6\text{ feet} \end{gathered}$

The value of x in the drawing is 6 feet.