Use the image to answer the 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)
To find the area of Annika's design, we need to calculate the individual areas of each shape and then add them together.
First, let's find the area of the rectangle. The length is 12 feet and the width is 4 feet, so the area of the rectangle is:
Area of rectangle = length x width = 12 feet x 4 feet = 48 square feet
Next, let's find the area of the right triangle. The base of the triangle is also 4 feet, and the height can be found by using the Pythagorean theorem:
(hypotenuse)^2 = (base)^2 + (height)^2
(4 feet)^2 = (4 feet)^2 + (height)^2
16 square feet = 16 square feet + (height)^2
(height)^2 = 16 square feet - 16 square feet
(height)^2 = 0 square feet
height = 0 feet
Since the height of the triangle is 0 feet, the area of the triangle is 0 square feet.
Finally, let's find the area of the square. The side length of the square is 4 feet, so the area of the square is:
Area of square = (side length)^2 = (4 feet)^2 = 16 square feet
Now, let's add up the areas of each shape to find the total area of Annika's design:
Total area = Area of rectangle + Area of triangle + Area of square
= 48 square feet + 0 square feet + 16 square feet
= 64 square feet
Therefore, the area of Annika's design is 64 square feet.