The area of the polygon (which represents the are of the home plate at the ball field) is given by: Option D: 39 in²
How to find the area of a region?
Supposing that there is no direct formula available for deriving the area, we can derive the area of that region by dividing it into smaller pieces, whose area can be known directly. Then summing all those pieces' area gives us the area of the main big region.
For this case, the area of the polygon is calculated as:
Area of polygon = Area of top triangle + Area of right sided triangle + Area of rectangle.
Now, we get:
- Part 1: Area of top triangle:
Top triangle has base 6 in (opposite sides of a rectangle are of same measure, so the bottom of the triangle is same as that of the opposite side to that base in the rectangle, which is of 6 inches). And height of 5 inches.
Thus, we get:
Area of the top triangle = [tex]\dfrac{1}{2} \times base \times height = \dfrac{1}{2} \times 6 \times 5 = 15 \: \rm in^2[/tex]
- Part 2: Area of right sided triangle:
Similar to above case, if we look horizontally, the base would be of 3 inches, and height is of 4 inches (for right sided triangle)
Thus, we get:
Area of the right sided triangle = [tex]\dfrac{1}{2} \times base \times height = \dfrac{1}{2} \times 3 \times 4 = 6 \: \rm in^2[/tex]
- Part 3: Area of the rectangle:
The rectangle has length 6 inches and width 3 inches.Thus, we get:Area of rectangle = [tex]length \times width = 6 \times 3 = 18 \: \rm in^2[/tex]
Thus, we get:
Area of polygon = Area of top triangle + Area of right sided triangle + Area of rectangle = 15 + 6 + 18 = 39 sq. inches
Thus, the area of the polygon (which represents the are of the home plate at the ball field) is given by: Option D: 39 in²
Learn more about total area of a figure here:
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