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Question

A composite shape is made up of a rectangle, triangle, and square. A horizontally aligned rectangle has a length of 12 feet and width of 4 feet. A right triangle adjoins the rectangle on the right side, with the vertical side common to the rectangle. A square with a side of 4 feet adjoins the right triangle along the bottom. Right angle marks are located in the four corners of the rectangle and the square, and also in the triangle where the base and vertical side meet.
Annika designs a hole for a miniature golf course. What is the area of Annika’s design in square feet?(1 point)
square feet

Answer 1

To calculate the area of Annika's composite shape, we need to find the area of the rectangle, the triangle, and the square separately, and then sum these areas.

1. Area of the Rectangle: \[ \text{Area}_{\text{rectangle}} = \text{length} \times \text{width} = 12 , \text{feet} \times 4 , \text{feet} = 48 , \text{square feet} \]

2. Area of the Triangle: The right triangle has a base equal to the width of the rectangle (4 feet) and a height equal to the height of the square (4 feet). \[ \text{Area}_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 4 , \text{feet} \times 4 , \text{feet} = \frac{1}{2} \times 16 , \text{square feet} = 8 , \text{square feet} \]

3. Area of the Square: The area of the square with a side of 4 feet is: \[ \text{Area}_{\text{square}} = \text{side}^2 = 4 , \text{feet} \times 4 , \text{feet} = 16 , \text{square feet} \]

4. Total Area: Now we sum the areas of the rectangle, triangle, and square: \[ \text{Total Area} = \text{Area}{\text{rectangle}} + \text{Area}{\text{triangle}} + \text{Area}_{\text{square}} \] \[ \text{Total Area} = 48 , \text{square feet} + 8 , \text{square feet} + 16 , \text{square feet} = 72 , \text{square feet} \]

Thus, the area of Annika's design is 72 square feet.