Composite Figure Area

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Answer Key & Explanations

Composite Figure Area · Grade 6 · Worksheet 3

1. A rectangular swimming pool measures 15 meters by 8 meters. A triangular concrete deck is attached to one of the longer sides of the pool, forming a right triangle with a base of 8 meters and height of 6 meters. What is the total area of the pool and deck combined? Answer: 144 Solution: Area of rectangle = length × width = 15 × 8 = 120 square meters Area of triangle = (1/2) × base × height = (1/2) × 8 × 6 = (1/2) × 48 = 24 square meters Total area = area of pool + area of deck = 120 + 24 = 144 square meters The answer is 144.
   Full step-by-step solution

   Step 1: Calculate the area of the rectangular pool Area of rectangle = length × width = 15 × 8 = 120 square meters Step 2: Calculate the area of the triangular deck Area of triangle = (1/2) × base × height = (1/2) × 8 × 6 = (1/2) × 48 = 24 square meters Step 3: Add the areas together Total area = area of pool + area of deck = 120 + 24 = 144 square meters The answer is 144.

2. Mere is designing a new school mural that has an L-shaped canvas. The main rectangular section measures 24 meters by 18 meters. Attached to one of the shorter sides is a smaller rectangular section measuring 12 meters by 8 meters. What is the total area of Mere's mural canvas in square meters? Answer: 528 Solution: Find the area of the main rectangular section. Area of main rectangle = length × width = 24 m × 18 m = 432 square meters. Find the area of the smaller rectangular section.
   Full step-by-step solution

   Step 1: Find the area of the main rectangular section. Area of main rectangle = length × width = 24 m × 18 m = 432 square meters. Step 2: Find the area of the smaller rectangular section. Area of small rectangle = length × width = 12 m × 8 m = 96 square meters. Step 3: Add the areas together to find the total area of the mural canvas. Total area = 432 + 96 = 528 square meters. The answer is 528.

3. Aroha's L-shaped garden is made from two rectangles: one is 13 m by 9 m and the other is 7 m by 5 m. What is the total area of the garden? Answer: 152 Solution: Find the area of the first rectangle: 13 × 9 = 117 square meters. Find the area of the second rectangle: 7 × 5 = 35 square meters. Add the two areas: 117 + 35 = 152 square meters.
   Full step-by-step solution

   Step 1: Find the area of the first rectangle: 13 × 9 = 117 square meters. Step 2: Find the area of the second rectangle: 7 × 5 = 35 square meters. Step 3: Add the two areas: 117 + 35 = 152 square meters. The total area of the garden is 152 square meters.

4. Sophia is helping her school design a new playground. The main play area is a rectangle that measures 32 meters by 24 meters. Attached to one of the longer sides is a triangular garden area that has a base of 16 meters and a height of 11 meters. What is the total area of Sophia's playground design in square meters? Answer: 856 Solution: Find the area of the rectangular play area. Area of rectangle = length × width = 32 m × 24 m = 768 square meters. Find the area of the triangular garden.
   Full step-by-step solution

   Step 1: Find the area of the rectangular play area. Area of rectangle = length × width = 32 m × 24 m = 768 square meters. Step 2: Find the area of the triangular garden. Area of triangle = 1/2 × base × height = 1/2 × 16 m × 11 m = 1/2 × 176 = 88 square meters. Step 3: Add the two areas to find the total area. Total area = 768 + 88 = 856 square meters. The answer is 856.