Question

The figure is drawn on centimeter grid paper. Find the perimeter of the shaded figure to the nearest tenth.

Answer 1

Answer:

17.6cm

Explanation:

We use the Pythagorean Theorem to find the length of the slant sides, x, and y in the diagram below:

$\begin{gathered} x^2=3^2+4^2 \\ x^2=25 \\ x^2=5^2 \\ x=5\operatorname{cm} \end{gathered}$

Similarly:

$\begin{gathered} y^2=3^2+7^2 \\ y^2=58 \\ y=\sqrt{58} \\ y=7.62\operatorname{cm} \end{gathered}$

Therefore, the perimeter of the shaded figure:

$\begin{gathered} P=1+y+x+4 \\ =1+7.62+5+4 \\ =17.62 \\ \approx17.6\operatorname{cm} \end{gathered}$