Problem 962

Find the k area of the triangle.

Solution:-

To find the area of the triangle, use the following theorem known as Heron’s Formula.

The area K of a triangle with sides a, b, and c is

K = $\sqrt{s(s-a)(s-b)(s-c)}$ , where s = $\frac{1}{2}$ (a+b+c).

First calculate the value of s as specified in the theorem.

s = $\frac{1}{2}$ (a+b+c)

= $\frac{1}{2}$ (2+6+7)

= $\frac{15}{2}$

Now use the Heron’s Formula to calculate the area.

K = $\sqrt {s (s-a)(s-b)(s-c)}$

= $\sqrt{\frac{15}{2}(\frac{15}{2}-2)(\frac{15}{2}-6)(\frac{15}{2}-7)}$

= $\sqrt{\frac{15}{2}*\frac{11}{2}*\frac{3}{2}*\frac{1}{2}}$

= $\sqrt{\frac{495}{16}}$

Simplify the right side to find the area of the triangle.

K $\approx$ 5.56 square units