Answer:
B. 24.28 square feet
Explanation:
To find the area of the entire composite figure, you will want to find the area of each shape in it and add them up. Personally, I like to start with the easiest one so in this case I would start with the rectangle.
To find the area of the rectangle, you must multiple length and width (l × w or b × h). So you would multiple 4ft by 3ft in this problem. The area of the rectangle then is 12 squared feet (12 ft²).
Next, find the area of the triangle using the formula 1/2×b×h (base= b; height= h). This is because since triangles are basically just squares and rectangles cut in half, all you would do it do the extra step of multiplying it by 1/2. In this problem, after substituting, you would get 1/2(4)(3). The area of the triangle then is 6 squared feet (6 ft²).
Finally, you want to find the area of the semi-circle. To do so, you must use the formula for finding the area of a circle which is π(r)². It is important to pay attention to what is given in the problem because of including the wrong number in your calculations.
In this problem, you are given the diameter of a circle, but what you need is the radius (per the circle area formula) so all you need to do it half it.
Diameter= 2r or Radius = 1/2D
This gives you the fact that the radius of a circle from this problem is 2 because the diameter is 4. HOWEVER, you need to remember that this problem is not asking you to include the area of a circle, it is asking for a semi-circle. This means that you would have to half the answer you get.
There are two easy ways of doing so for this case like:
1/2 π(2)² 1/4 π (2)²
Just plug either equation into the calculator and have it solved to have the area of the semi-circle.
The last and easiest step is just adding all 3 areas calculated to get the approximate total area of the figure!
12+6+6.28= 24.28 squared feet (24.28 ft ²)