Question

Find the area of a triangle ABC when c = 15 m, a = 20 meters, andb = 10 meters.

Answer 1

EXPLANATION

Since we have the given sides, we can apply the Heron's Formula in order to obtain the value of the area:

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

Where s represents the semiperimeter with the following formula:

$Semiperimeter=\frac{a+b+c}{2}$

Plugging in the terms into the expression:

$Semiperimeter=\frac{20+10+15}{2}$

Adding numbers::

$Semiperimeter=\frac{45}{2}$

Simplifying:

$Semiperimeter=s=22.5$

Plugging in the semiperimeter into the expression:

$Area=\sqrt{22.5(22.5-20)(22.5-10)(22.5-15)}$

Subtracting and multiplying numbers:

$Area=\sqrt{22.5(2.5)(12.5)(7.5)}$

Multiplying numbers:

$Area=\sqrt{5273.43}$

Computing the root:

$Area=72.61m^2$

In conclusion, the area is 72.61m^2