Question

what is the area of the pentagon shown?
a.150cm^2
b.100 cm^2
c. 80cm^2
d.120cm^2​

Answer 1

We can divide the pentagon into a rectangle (on the left) and a triangle (on the right)

The dimensions of the rectangle are 8x10 cm, so its area is

$8\cdot 10=80\text{ cm}^2$

The triangle has the same base as the rectangle, and its height is the difference between the sides of 15 and 10: the area is

$\dfrac{8\cdot (15-10)}{2} = 4\cdot 5 = 20\text{ cm}^2$

So, the total area is

$80\text{ cm}^2+20\text{ cm}^2=100\text{ cm}^2$