Question

Estimate the perimeter and the area of the shaded figure to the nearest whole number.

Answer 1

Perimeter:

`about \: 12 \: \: units`

Area:

`about \: 21 \: {units} ^(2)`

Explanation:

The perimeter of this shape would be the value of all the sides added together. The sides measure: 4 units, 4 units, 1 unit, 1 unit, 1 unit, 1 unit. Therefore the perimeter is: 12 units

`4 + 4 + 1 + 1 + 1 + 1 = 12`

To find the area of the shape we have to split it into a square and 2 triangles. The formula to find the area of a square is

`a = length * width \: or \: {(side)}^(2)`

All sides of a square are equal and the side measures 4 units, hence the area is

`{4} ^(2) = 16`

The formula to find the area of a triangle is

`(1)/(2) base \: * height`

Both triangles are equal and as such after finding the area of one triangle you can just multiply it by 2. The base is 3 units and the height is 1.5 units.

`(1)/(2) b * h \\ (1)/(2) (3) * 1.5 \\ 1.5 * 1.5 = 2.25 \\ 2.25 * 2 = 4.5`

`area \: or \: square \: + area \: of \: 2 \: triangles \\ 16 + 4.5 = 20.5 \: or \: 21 (whole\: number)`

Answer 2

Explanation:

The area and perimeter of the given shaded figure are respectively 33.12 unit² and 20.56 units.

Area and perimeter-based problem:

What information do we have?

Radius of semi-circle = 8 / 2 = 4 unit

Length of remain Rectangle = 8 unit

Width of remain Rectangle = 2 unit

Perimeter of shaded figure = πr + (l + 2b)

Perimeter of shaded figure = (3.14)(4) + [4 + (2)(2)]

Perimeter of shaded figure = 12.56 + 4 + 4

Perimeter of shaded figure = 20.56 units

Area of shaded figure = πr²/2 + lb/2

Area of shaded figure = (3.14)(4)²/2 + (8)(2)/2

Area of shaded figure = (3.14)(8) + 8

Area of shaded figure = 25.12 + 8

Area of shaded figure = 33.12 unit²