Chapter 11.4, Problem 5ST1

To determine

To find: The area of the polygon.

Answer to Problem 5ST1

  $A=6\sqrt{13}sq.unit$

Explanation of Solution

Given: An isosceles triangle with sides $7,7,12$ .

Finding the area using the heron’s formula

  $\begin{array}{l}Sides=7,7,12\\ a=7,b=7,c=12\\ s=\frac{1}{2}(a+b+c)\\ s=\frac{1}{2}(7+7+12)\\ s=13cm\\ now\\ A=\sqrt{s(s-a)(s-b)(s-c)}\\ A=\sqrt{13(13-7)(13-7)(13-12)}\\ A=\sqrt{13(6)(6)(1)}\\ A=6\sqrt{13}sq.unit\end{array}$

Hence, $A=6\sqrt{13}sq.unit$