Answer :

charlief22

Answer:

 [tex]26.13ft^2[/tex]

Step-by-step explanation:

Step  1 - As both triangles have lengths the same size, they both add together to equal a rectangle. Therefore:

4 x 3 = 12

Which is the area of the triangles.

Step 2 - Calculating the area of a circle uses the formula:

[tex]\pi r^2[/tex]

Where r is the radius of the circle.

Plug the known variables in:

[tex]\pi \cdot 3^2\\\pi \cdot 9\\3.14 \cdot 9 = 28.26\\[/tex]

However, this is the area of a full circle. The figure is only half a circle so we must divide this by two:

28.26 ÷ 2 = 14.13

Now, add the area of the semi-circle to the area of the triangles:

14.13 + 12 = 26.13

Therefore, the area of the figure is [tex]26.13ft^2[/tex].

Hope this helps!

Solution:

Given:

  • Radius of circle = 3 ft.
  • Height of triangle = 4 ft.

1. Finding the area of the semi-circle:

Since the area of the semi-circle is the area of half the circle, the formula of finding the area of the circle will be divided by 2 to find the area of the semi-circle.

This means that:

  • Area of semi-circle = Area of circle/2 = πr²/2

Now, let's substitute the radius into the formula to find the area.

Substituting the radius into the equation:

  • Area of semi-circle = πr²/2
  • => Area of semi-circle = (π)(3²)/2

Simplifying the RHS:

  • => Area of semi-circle = (π)(3²)/2
  • => Area of semi-circle = (π)(9)/2

Substituting π as 3.14:

  • => Area of semi-circle = (π)(9)/2
  • => Area of semi-circle = (3.14)(9)/2

Simplifying the RHS:

  • => Area of semi-circle = (3.14)(9)/2
  • => Area of semi-circle = (1.57)(9)
  • => Area of semi-circle = 14.13

2. Finding the area of the triangle:

Before we find the area of the triangle, we need to know the base, which is the diameter of the semi-circle.

  • Diameter = 2(Radius)
  • => Diameter = 2(3)
  • => Diameter = 6 feet

Now, let's find the area of the triangle.

  • Area of triangle = 1/2 x 6 x 4
  • => Area of triangle = 3 x 4
  • => Area of triangle = 12 ft²

3. Finding the area of the figure:

The area of the figure is basically the sum of the semi-circle and the triangle.

  • => Area of figure = Area of triangle + Area of semi-circle
  • => Area of figure = 12 + 14.13
  • => Area of figure = 26.13 ft²

Thus, the area of the figure is 26.13 ft².

If you have any questions or any confusions, post them in the comments.

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