Question

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what is the perimeter of the composite figure?
round your answer to the nearest hundredth.
enter your answer in the box.
perimeter = cm²

Explanation:

Step1: Find the height of the triangle

The total height of the figure is \(18\) cm and the height of the rectangle is \(10\) cm. So the height of the triangle \(h = 18 - 10=8\) cm.

Step2: Find the length of the slant side of the triangle

The base of the triangle is \(5\) cm. Using the Pythagorean theorem \(a=\frac{5}{2} = 2.5\) cm (half - base of the triangle), and \(h = 8\) cm. The length of the slant side \(l=\sqrt{a^{2}+h^{2}}=\sqrt{2.5^{2}+8^{2}}=\sqrt{6.25 + 64}=\sqrt{70.25}\approx8.38\) cm.

Step3: Calculate the perimeter of the composite figure

The perimeter of the composite figure is composed of two lengths of the rectangle (\(10\) cm each), two slant sides of the triangle (\(l\approx8.38\) cm each), and the base of the rectangle (\(5\) cm).
\(P=10 + 10+8.38+8.38 + 5\)
\(P=(10 + 10+5)+(8.38+8.38)\)
\(P = 25+16.76\)
\(P=41.76\) cm

Answer:

\(41.76\)