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)

Answer 1

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

1. **Area of the Rectangle:**
- Length = 12 feet
- Width = 4 feet
- Area = Length × Width = 12 × 4 = 48 square feet

2. **Area of the Square:**
- Side = 4 feet
- Area = Side × Side = 4 × 4 = 16 square feet

3. **Area of the Triangle:**
- The triangle is a right triangle attached to the rectangle with a vertical side that is the same as the rectangle’s height, which is 4 feet. The base of the triangle is equal to the width of the square, which is also 4 feet.
- Base = 4 feet (the bottom side of the triangle)
- Height = 4 feet (the vertical side of the triangle)
- Area = (1/2) × Base × Height = (1/2) × 4 × 4 = 8 square feet

4. **Total Area of the Composite Shape:**
- Total Area = Area of Rectangle + Area of Square + Area of Triangle
- Total Area = 48 + 16 + 8 = 72 square feet

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