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

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Answer 1 · 2015-11-21T01:04:33

Area #=48# #cm^2#

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#.