Respuesta :

MeiMae

Answer:

B. (8π + 12) in²

Step-by-step explanation:

1. Identify the formula for the area of both a triangle and a circle.

    Triangle: 1/2(b)(h)

       b = base

       h = height

    Circle: πr²

      r = radius

2. Start by finding the area of the circle, since we already have all the needed information for the variables in the equation.

     π(4)² → π(16) → 16π

3. Half the answer we just got as the area of the circle. We are doing this because we only have half a circle in the diagram, and we solved for the area of a full circle.

    (16π)/2 → 8π

4. Next find the base of the triangle, since this is the only information we do not yet have for the triangle. We will find this by doubling the 4, since 4 inches is only half the length of the base.

    4 × 2 = 8

5. Plug all the information of the triangle into the area of a triangle formula and solve.

    1/2(8)(3) → 1/2(24) → 12

6. Add both the area of the semi-circle and triangle together because they are one shape that we are finding the area for.

     8π + 12  

7. Label answer with units of measurement

    (8π + 12) in²            

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ANSWER

The correct option is B

EXPLANATION

The composite figure is made up of a semicircle and an isosceles triangle.

The area of a semicircle is

[tex] \frac{1}{2}\pi {r}^{2} [/tex]

From the diagram, the radius is

[tex]r = 4 \: in[/tex]

When we substitute, area of the semicircle is

[tex] \frac{1}{2} \times \pi \times {4}^{2} [/tex]

[tex]\frac{1}{2} \times \pi \times 16[/tex]

[tex]8\pi \: \: {in}^{2} [/tex]

The area of the isosceles triangle is

[tex] \frac{1}{2} \times base \times height[/tex]

[tex] = \frac{1}{2} \times (4 + 4) \times 3[/tex]

[tex] = \frac{1}{2} \times 8 \times 3[/tex]

[tex] = 12 \: {in}^{2} [/tex]

We add the two areas to obtain the area of the composite figure to be:

[tex](8\pi + 12) {in}^{2} [/tex]

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