Use the Pythagorean Theorem to find 'h'.
[tex]\sf a^2+b^2=c^2[/tex]
For right triangles, where 'a' and 'b' are the two legs and 'c' is the hypotenuse.
Divide the base by 2 to find the base length of one of the right triangles. 32/2 = 16. Now apply the Pythagorean Theorem:
[tex]\sf 16^2+b^2=20^2[/tex]
Simplify:
[tex]\sf 256+b^2=400[/tex]
Subtract 256 to both sides:
[tex]\sf b^2=144[/tex]
Take the square root of both sides:
[tex]\sf b = 12[/tex]
So the height is 12cm. Apply the formula for the area of a triangle:
[tex]\sf A=\frac{1}{2}bh[/tex]
[tex]\sf A=\frac{1}{2}(32)(12)[/tex]
[tex]\sf A=192cm^2[/tex]
