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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)

1 answer

To find the area of Annika's composite design consisting of a rectangle, triangle, and square, we can calculate the area of each individual shape and then sum them up.

  1. Area of the Rectangle:

    • Length = 12 feet
    • Width = 4 feet
    • Area = Length × Width = 12 feet × 4 feet = 48 square feet

  2. Area of the Square:

    • Side = 4 feet
    • Area = Side × Side = 4 feet × 4 feet = 16 square feet

  3. Area of the Triangle:

    • The triangle is a right triangle. We need to find the base and height.
    • The base is the same as the width of the rectangle (4 feet).
    • The height is the same as the height of the square (4 feet).
    • Area = (Base × Height) / 2 = (4 feet × 4 feet) / 2 = 16 square feet

  4. Total Area:

    • Total Area = Area of Rectangle + Area of Square + Area of Triangle
    • Total Area = 48 square feet + 16 square feet + 16 square feet = 80 square feet

Therefore, the area of Annika's design is 80 square feet.