Composite Figure Area

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Answer Key & Explanations

Composite Figure Area · Grade 6 · Worksheet 2

1. Sophia is creating a large mosaic for a community art project. The mosaic has an L-shaped design made from two rectangular sections. The main rectangular section measures 18 feet by 12 feet. Attached to the right side of this main rectangle is a smaller rectangular section that measures 9 feet by 7 feet. What is the total area of Sophia's mosaic in square feet? Answer: 279 Solution: Find the area of the main rectangular section. Area = length × width = 18 ft × 12 ft = 216 square feet Find the area of the smaller rectangular section.
   Full step-by-step solution

   Step 1: Find the area of the main rectangular section. Area = length × width = 18 ft × 12 ft = 216 square feet Step 2: Find the area of the smaller rectangular section. Area = length × width = 9 ft × 7 ft = 63 square feet Step 3: Add the areas together. Total area = 216 + 63 = 279 square feet The answer is 279.

2. Sophia is designing a large rectangular mural for the school gymnasium. The mural is 26 feet wide and 16 feet tall. She decides to add a triangular section on top of the mural that has the same width as the rectangle and a height of 11 feet. What is the total area of Sophia's mural design in square feet? Answer: 559 Solution: Find the area of the rectangular section. Area of rectangle = width × height = 26 ft × 16 ft = 416 square feet. Find the area of the triangular section.
   Full step-by-step solution

   Step 1: Find the area of the rectangular section. Area of rectangle = width × height = 26 ft × 16 ft = 416 square feet. Step 2: Find the area of the triangular section. The base of the triangle is the same as the width of the rectangle, 26 ft. Area of triangle = 1/2 × base × height = 1/2 × 26 ft × 11 ft = 1/2 × 286 = 143 square feet. Step 3: Add the areas together. Total area = 416 + 143 = 559 square feet. The answer is 559.

3. Kaia's L-shaped garden is made from two rectangles: one measuring 14 m by 9 m and the other measuring 11 m by 6 m. What is the total area of the garden? Answer: 192 Solution: Find the area of the first rectangle: 14 × 9 = 126 square meters. Find the area of the second rectangle: 11 × 6 = 66 square meters. Add the two areas: 126 + 66 = 192 square meters.
   Full step-by-step solution

   Step 1: Find the area of the first rectangle: 14 × 9 = 126 square meters. Step 2: Find the area of the second rectangle: 11 × 6 = 66 square meters. Step 3: Add the two areas: 126 + 66 = 192 square meters. The total area of the garden is 192 square meters.

4. Noah is designing a new skatepark with a composite shape. The main area is a rectangle that measures 42 meters by 28 meters. On one of the shorter sides, there is a triangular extension for a beginner's area that has a base of 14 meters and a height of 10 meters. What is the total area of Noah's skatepark design in square meters? Answer: 1246 Solution: Area of rectangle = length × width = 42 m × 28 m = 1176 square meters Area of triangle = 1/2 × base × height = 1/2 × 14 m × 10 m = 1/2 × 140 = 70 square meters Total area = area of rectangle + area of triangle = 1176 + 70 = 1246 square meters The answer is 1246.
   Full step-by-step solution

   Step 1: Calculate the area of the rectangular section Area of rectangle = length × width = 42 m × 28 m = 1176 square meters Step 2: Calculate the area of the triangular section Area of triangle = 1/2 × base × height = 1/2 × 14 m × 10 m = 1/2 × 140 = 70 square meters Step 3: Add the areas together to find the total area Total area = area of rectangle + area of triangle = 1176 + 70 = 1246 square meters The answer is 1246.