What is the area of an isosceles triangle with two equal sides of 10 cm and a base of 12 cm?

1 Answer
Nov 21, 2015

Area =48 cm^2

Explanation:

Since an isosceles triangle has two equal sides, if the triangle is split in half vertically, the length of the base on each side is:

12 cm-:2 = 6 cm

We can then use the Pythagorean theorem to find the height of the triangle.

The formula for the Pythagorean theorem is:

a^2+b^2=c^2

To solve for the height, substitute your known values into the equation and solve for a:

where:
a = height
b = base
c = hypotenuse

a^2+b^2=c^2
a^2=c^2-b^2
a^2=(10)^2-(6)^2
a^2=(100)-(36)
a^2=64
a=sqrt(64)
a=8

Now that we have our known values, substitute the following into the formula for area of a triangle:

base = 12 cm
height = 8 cm

Area=(base*height)/2

Area=((12)*(8))/2

Area=(96)/(2)

Area=48

:., the area is 48 cm^2.