Question

The trapezoid above is cut into two triangles with a black line. Find the area of the two triangles and add the areas together. (HINT: Don't forget that you have to divide by 2 for the area of triangles!) No labels.

Answer 1

`42`

Explanation:

The area of a triangle with base
`b` and height
`h` is given by
`A=(1)/(2)bh`. In the trapezoid, the two triangles share a height of 6, however one has a base of 6 and the other has a base of 8.

Area of smaller triangle (triangle on the left):
`(1)/(2)\cdot 6 \cdot 6=18\:\mathrm{cm^2}`

Area of larger triangle (triangle on the right):
`(1)/(2)\cdot 8 \cdot 6=24\:\mathrm{cm^2}`

Therefore, the sum of their areas are
`18+24=\boxed{42\:\mathrm{cm^2}}`

Answer 2

Explanation:

The triangle on the left is going to be a little trickier than the one on the right.

Right

height = 6

base = 8

Area = 1/2 * 6 * 8 = 24

Left

h=6

base = 6

Area = 1/2 * 6 * 6

Area = 18

Total Area = 18 + 24 = 42