Chapter 11.2, Problem 11E

To determine

To Find: Use two different method to find the exact area of the triangle.

Answer to Problem 11E

  $A=60sq.unit$

Explanation of Solution

Given: The sides of a triangle are given.

  $13,13,10$

Given: $13,13,10$

i.e.

  $a=13,b=13,c=10$

Using Heron’s formula

  $\begin{array}{l}s=\frac{1}{2}(a+b+c)\\ s=\frac{1}{2}(13+13+10)\\ s=18\\ now\\ A=\sqrt{s(s-a)(s-b)(s-c)}\\ A=\sqrt{18(18-13)(18-13)(18-10)}\\ A=\sqrt{18(5)(5)(8)}\\ A=60sq.unit\end{array}$

Using area of triangle formula

Using Pythagoras theorem

  $\begin{array}{l}{13}^2=h^2+5^2\\ h^2=169-25=144\\ h=12\end{array}$

  $\begin{array}{l}A=\frac{1}{2}bh\\ A=\frac{1}{2}(10)(12)\\ A=60\end{array}$

Hence, $A=60sq.unit$