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.

Explanation:

Using the area formula of the trapezium,

$\begin{gathered} A=\frac{1}{2}(a+b)h \\ =\frac{1}{2}(4+6)\times8 \\ =\frac{1}{2}\times10\times8 \\ A=40mm^2 \end{gathered}$

Let us the length of the slant height.

Using the Pythagoras theorem,

$\begin{gathered} hyp^2=opp^2+adj^2 \\ hyp^2=8^2+2^2 \\ hyp^2=64+4 \\ hyp^2=68 \\ hyp=\sqrt{68} \\ hyp=8.246 \\ hyp\approx8.25 \end{gathered}$

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.