Question

Find the area of this figure. round your answer to the nearest hundredth. use 3.14 to approximate pi

Answer 1

Step-1: Find the area of the triangle.

`\text{Area of triangle} = (1)/(2) * \text{Base} * \text{Height}`

`\text{Area of triangle} = (1)/(2) * 3 * 5`

`\text{Area of triangle} = 3 * 2.5`

`\text{Area of triangle} = 7.5 \ \text{m}^(2)`

Step-2: Find the area of the rectangle.

`\text{Area of rectangle} = \text{LB}`

`\text{Area of rectangle} = (6)(5)`

`\text{Area of rectangle} = 30 \ \text{m}^(2)`

Step-3: Find the radius of the semi-circle.

`\text{Diameter = 2(Radius)}`

`6 \ \text{m = 2(Radius)}`

`(6)/(2) \ \text{m} = \frac{2\text{(Radius)}}{2}`

`3 \ \text{m} = \text{Radius}`

Step-4: Find the area of the semi-circle.

`\text{Area of semi-circle} = (\pi r^(2) )/(2)`

`\text{Area of semi-circle} = ((3.14)( 3^(2) ))/(2)`

`\text{Area of semi-circle} = ((3.14)(9 ))/(2)`

`\text{Area of semi-circle} = (3.14)(4.5 )`

`\text{Area of semi-circle} = 14.13 \ \text{m}^(2)`

Step-5: Find the area of the figure.

`\text{Area of figure = Area of triangle + Area of rectangle + Area of semicircle}`

`\text{Area of figure = 7.5 + 30 + 14.13}`

`\boxed{\text{Area of figure = 51.63 m}^(2)}`

Answer 2

51.63 m²

Explanation:

`\textsf{Area of a semicircle} =\frac12\pi r^2`

Given:

• 
  `\pi =3.14`
• 
  `\textsf{diameter}=6 \textsf{ m}\implies \textsf{radius}=3 \textsf{ m}`

`\implies \textsf{area}=\frac12 * 3.14 * 3^2=14.13`

`\textsf{Area of a triangle} =\frac12 * \textsf{base} * \textsf{height}`

Given:

• base = 3 m
• height = 5 m

`\implies \textsf{area}=\frac12 * 3 * 5=7.5`

`\textsf{Area of a rectangle} =\textsf{width} * \textsf{length}`

Given:

• width = 5 m
• length = 6 m

`\implies \textsf{area}=5 * 6=30`

Total area = area of semicircle + area of triangle + area of rectangle

= 14.13 + 7.5 + 30

= 51.63 m²