Question

Find the area of the irregular figure. Round to the nearest hundredth.

Answer 1

Answer:

$67.5\text{ [square units]}$

Step-by-step explanation:

The composite figure consists of one rectangle and two triangles. We can add up the area of these individual shapes to find the total area of the irregular figure.

Formulas:

• Area of rectangle with base $b$ and height $h$: $A=bh$
• Area of triangle with base $b$ and height $h$: $A=\frac{1}{2}bh$

By definition, the base and height must intersect at a 90 degree angle.

The rectangle has a base of 10 and a height of 5. Therefore, its area is $A=10\cdot 5=50$.

The smaller triangle to the left of the rectangle has a base of 2 and a height of 5. Therefore, its area is $A=\frac{1}{2}\cdot 2\cdot 5=5$.

Finally, the larger triangle on top of the rectangle has a base of 5 and a height of 5. Therefore, its area is $A=\frac{1}{2}\cdot 5\cdot 5=12.5$.

Thus, the area of the total irregular figure is:

$50+5+12.5=\boxed{67.5\text{ [square units]}}$