Question

The base of an isosceles triangle is 16 centimeters, and the equal sides have length 18 centimeters. Suppose we increase the base of the triangle to 19 while holding the sides constant. What is the area?

Answer 1

Area = 145.244 centimeter`s^2`

Explanation:

If we need to calculate area just according to second value of base i.e. 19 centimeters, we will do all the calculations with that value only.

To calculate area of isosceles triangle, first we need to find the measure of its height.

When we cut isosceles triangle in half, we will get two identical right-triangles with base`=19/2=9.5` centimeters and hypotenuse`=18` centimeters . The perpendicular of these right-triangles will also be the height of actual isosceles triangle. We can calulate length of this perpendicular side using Pythagoras Theorem which says:

Hypotenus`e^2=Base^2+`Perpendicula`r^2`
Perpendicular`=sqrt(Hyp^2-Base^2)=sqrt(18^2-9.5^2)=15.289`

So, height of isosceles triangle`=15.289` centimeters

Area`=1/2xxBasexxHeight=1/2xx19xx15.289=145.2444`