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

##### 1 Answer

Area

#### 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

where:

#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:

#Area=(base*height)/2#

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

#Area=(96)/(2)#

#Area=48#