Question

Find the area of the shaded region. Round to the nearest hundredth when necessary.

Answer 1

The shaded area is 223.72 square units in size.

Area of the triangle - Area of the parallelogram = area of the shaded area.

Area of the parallelogram = base x height

= 15.2 x 23.8

= 357 square feet

Area of triangle = 1/2 base x height

Using the Pythagorean theorem, let h represent the triangle's height;

23.8² = 21² + h²

566.44 = 441 + h²

h² = 125.44

h = 11.2

Area of Triangle = 1/2 x 23.8 x 11.2.

= 133.28

Area of shaded region = 357 - 133.28

= 223.72

Area of the shaded region is 223.72 square units.

Answer 2

Area of the shaded region is 223.72 square units.

Explanation:

Area of the shaded region = Area of parallelogram - Area of triangle

Area of the parallelogram = base x height

= 23.8 x 15

= 357 square feet

Area of triangle =
`(1)/(2)` x base x height

Let the height of the triangle be represented by h, applying the Pythagoras theorem;

`23.8^(2)` =
`21^(2)` +
`h^(2)`

566.44 = 441 +
`h^(2)`

`h^(2)` = 125.44

h =
`√(125.44)`

= 11.2

h = 11.2

Area of the triangle =
`(1)/(2)` x 23.8 x 11.2

= 133.28

Area of shaded region = 357 - 133.28

= 223.72

Area of the shaded region is 223.72 square units.