Question

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

Answer 1

Answer:

51.63 m²

Step-by-step explanation:

$\textsf{Area of a semicircle} =\dfrac12\pi r^2$

Given:

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

$\implies \textsf{area}=\dfrac12 \times 3.14 \times 3^2=14.13$

$\textsf{Area of a triangle} =\dfrac12 \times \textsf{base} \times \textsf{height}$

Given:

• base = 3 m
• height = 5 m

$\implies \textsf{area}=\dfrac12 \times 3 \times 5=7.5$

$\textsf{Area of a rectangle} =\textsf{width} \times \textsf{length}$

Given:

• width = 5 m
• length = 6 m

$\implies \textsf{area}=5 \times 6=30$

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

                 = 14.13 + 7.5 + 30

                  = 51.63 m²

Answer 2

Solution:

Step-1: Find the area of the triangle.

$\text{Area of triangle} = \dfrac{1}{2} \times \text{Base} \times \text{Height}$

$\text{Area of triangle} = \dfrac{1}{2} \times 3 \times 5$

$\text{Area of triangle} = 3 \times 2.5$

$\text{Area of triangle} = 7.5 \ \text{m}^{2}$

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.

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

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

$\dfrac{6}{2} \ \text{m} = \dfrac{2\text{(Radius)}}{2}$

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

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

$\text{Area of semi-circle} = \dfrac{\pi r^{2} }{2}$

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

$\text{Area of semi-circle} = \dfrac{(3.14)(9 )}{2}$

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

$\text{Area of semi-circle} = 14.13 \ \text{m}^{2}$

Step-5: Find the area of the figure.

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

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

$\boxed{\text{Area of figure = 51.63 m}^{2}}$