Question

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

Answer 1

`67.5\text{ [square units]}`

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=(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=(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=(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]}}`