Question

the perimeter of the polygon shown in the figure is _.
15 units
30 units
2√34 + 6units
204 units

Explanation:

Step1: Find the lengths of the sides

Assume the coordinates of the vertices of the triangle. Let's say two sides are right - angled. One side has length \(6\) units (vertical side) and another side (horizontal side) has length \(8\) units. Using the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}\) for the hypotenuse. For \(a = 6\) and \(b=8\), \(c=\sqrt{6^{2}+8^{2}}=\sqrt{36 + 64}=\sqrt{100}=10\) units.

Step2: Calculate the perimeter

The perimeter \(P\) of a triangle is \(P=a + b + c\). Here \(a = 6\), \(b = 8\) and \(c = 10\). So \(P=6+8 + 10=30\) units.

Answer:

30 units