Question

I need help with finding areas and perimeter for a trapezoid thank you

Answer 1

Given:

The length of the parallel sides are

`\begin{gathered} a=4mm \\ b=6mm \end{gathered}`

The altitude is,

`h=8mm`

To find:

The area and perimeter of the trapezium.

Step-by-step explanation:

Using the area formula of the trapezium,

`\begin{gathered} A=(1)/(2)(a+b)h \\ =(1)/(2)(4+6)*8 \\ =(1)/(2)*10*8 \\ A=40mm^2 \end{gathered}`

Let us the length of the slant height.

Using the Pythagoras theorem,

`\begin{gathered} hyp^2=opp^2+adj^2 \\ hyp^2=8^2+2^2 \\ hyp^2=64+4 \\ hyp^2=68 \\ hyp=√(68) \\ hyp=8.246 \\ hyp\approx8.25 \end{gathered}`

Therefore, the length of the slant height is 8.25mm.

Using the perimeter formula,

`\begin{gathered} Perimeter=Sum\text{ of all sides' length} \\ P=4+8.25+6+8 \\ P=26.25mm \end{gathered}`

Final answer:

The area of the trapezium is 40 square mm.

The perimeter of the trapezium is 26.25 mm.