math 7th grade connexus Area of Composite Figures practice

Answer 1

Sure! Here are some practice problems involving the area of composite figures suitable for 7th-grade math.

Problem 1

A rectangular garden measures 10 meters by 5 meters. Next to it, there is a semicircular fountain with a diameter of 4 meters. Find the total area of the garden and the fountain combined.

Problem 2

A composite figure consists of a rectangle that is 8 cm long and 4 cm wide, attached to a triangle with a base of 4 cm and a height of 3 cm. Calculate the total area of the figure.

Problem 3

A playground is made up of a rectangular area measuring 15 m by 10 m and a triangular sandbox with a base of 5 m and a height of 4 m. What is the total area of the playground?

Problem 4

A composite figure is formed by combining a square with a side length of 6 feet and a triangle with a base of 6 feet and a height of 5 feet. What is the total area of the composite figure?

Problem 5

A building's roof is designed as a composite figure with a rectangular central part that measures 12 ft by 10 ft and two triangular sections at the ends, each with a base of 10 ft and a height of 6 ft. Find the total area of the roof.

Solutions

Here are the steps to solve these problems:

1. Problem 1

   • Area of the rectangle = length × width = 10 m × 5 m = 50 m².
   • Area of the semicircle = (1/2) × π × radius²; radius = diameter/2 = 4 m/2 = 2 m.
   • Area of the semicircle = 1/2 × π × (2 m)² ≈ 6.28 m².
   • Total area = 50 m² + 6.28 m² ≈ 56.28 m².

2. Problem 2

   • Area of the rectangle = length × width = 8 cm × 4 cm = 32 cm².
   • Area of the triangle = (1/2) × base × height = (1/2) × 4 cm × 3 cm = 6 cm².
   • Total area = 32 cm² + 6 cm² = 38 cm².

3. Problem 3

   • Area of the rectangle = length × width = 15 m × 10 m = 150 m².
   • Area of the triangle = (1/2) × base × height = (1/2) × 5 m × 4 m = 10 m².
   • Total area = 150 m² + 10 m² = 160 m².

4. Problem 4

   • Area of the square = side × side = 6 ft × 6 ft = 36 ft².
   • Area of the triangle = (1/2) × base × height = (1/2) × 6 ft × 5 ft = 15 ft².
   • Total area = 36 ft² + 15 ft² = 51 ft².

5. Problem 5

   • Area of the rectangle = length × width = 12 ft × 10 ft = 120 ft².
   • Area of one triangle = (1/2) × base × height = (1/2) × 10 ft × 6 ft = 30 ft².
   • Total area of two triangles = 30 ft² × 2 = 60 ft².
   • Total area = 120 ft² + 60 ft² = 180 ft².

Feel free to ask for more problems or clarification on any concept!