Mia’s model for a dress is shown. The model is composed of a trapezoid and a rectangle with a semi-circle taken out of it.
What is the area of Mia’s model for a dress?
Responses
A 2.5 ft22.5 ft 2
B 2.9 ft22.9 ft 2
C 2.1 ft22.1 ft 2
D 3.3 ft23.3 ft 2
To find the area of Mia's dress model, we need to find the individual areas of the trapezoid, rectangle, and semi-circle, and then add them together.
The area of a trapezoid is given by the formula A = (1/2)(a + b)h, where a and b are the lengths of the parallel sides and h is the height.
In this case, the parallel sides of the trapezoid are 3 ft and 1 ft, and the height is 4.5 ft.
So, the area of the trapezoid is A = (1/2)(3 + 1)(4.5) = 2(4.5) = 9 ft^2.
The area of a rectangle is given by the formula A = l*w, where l is the length and w is the width.
In this case, the length of the rectangle is 3 ft and the width is 4.5 ft.
So, the area of the rectangle is A = 3(4.5) = 13.5 ft^2.
The area of a semi-circle is given by the formula A = (πr^2)/2, where r is the radius.
In this case, the radius of the semi-circle is 1.5 ft.
So, the area of the semi-circle is A = (3.14*1.5^2)/2 = 3.525 ft^2.
Now, we can add the individual areas together:
9 ft^2 + 13.5 ft^2 + 3.525 ft^2 = 26.025 ft^2.
Therefore, the area of Mia's dress model is approximately 26.025 ft^2.
The correct answer is not given in the options.