Question

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

Answer 1

X=6

Explanation:

First multiply 8 by 16 to get 128. Then subtract that from 176 to get 48. Then divide by to because there are two triangles to get 24, so each triangle is 24 square feet. Find a number that multiplied by 8 equals 48 (this will be x). The reason that I did this is because of the formula for area of a triangle (B*H/2=A). After you divide by 48 by 2 you will get 24. The number that was multiplied by 8 is x (x=6).

Answer 2

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=(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=(1)/(2)*8(16+16+2x) \\ 176=4(32+2x) \end{gathered}`

Divide both sides by 4.

`\begin{gathered} (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} (12)/(2)=(2x)/(2) \\ x=6\text{ feet} \end{gathered}`

The value of x in the drawing is 6 feet.