Area of Composite Shapes

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Show your work for each problem.

1.
What is the first step when finding the area of a composite shape?
1. a)Draw a circle around the shape
2. b)Add all the sides together
3. c)Identify the basic shapes within the composite shape
4. d)Multiply length times width
2.
A rectangle with a circular hole cut out of it requires you to:
1. a)Add the circle area to the rectangle area
2. b)Multiply the areas together
3. c)Subtract the circle area from the rectangle area
4. d)Divide the rectangle area by the circle area
3.
An L-shaped figure is made of two rectangles: one is m by m and the other is m by m. What is the total area in m²?
4.
A house-shaped figure has a square base with side m and a triangular roof with base m and height m. What is the total area in m²?
5.
Find the area of a rectangle ( cm by cm) with a triangular extension (base cm, height cm).
6.
A rectangle measures m by m with a circular pool of radius m in the center. Using , what is the area of the lawn (excluding the pool)?
1. a) m²
2. b) m²
3. c) m²
4. d) m²
7.
A metal sheet is cm by cm with a square hole of side cm cut out. What is the remaining area in cm²?
8.
A wall is m wide and m tall with a triangular gable (base m, height m) on top. Find the total wall area.
9.
An arrow-shaped sign has a rectangle ( cm by cm) with a triangle on one end (base cm, height cm). What is the total area in cm²?
10.
A sign is a rectangle ( cm by cm) with TWO triangular points, one on each short end. Each triangle has base cm and height cm. Find the total area.
11.
A square courtyard ( m side) has a rectangular garden ( m by m) and a circular fountain (radius m) inside. Using , what is the remaining paved area?
1. a) m²
2. b) m²
3. c) m²
4. d) m²
12.
A T-shaped platform consists of three rectangles: a horizontal bar ( m by m) and a vertical stem ( m by m). What is the total area in m²?
13.
A window consists of a rectangle ( m by m) with a semicircular top (diameter m). Using , find the total glass area.
14.
A hexagonal nut has a hexagonal outer boundary that can be approximated as a square ( cm side) with four corner triangles (each with legs cm). The circular hole in the center has radius cm. Using , find the metal area to 2 decimal places.
15.
A running track is a rectangle ( m by m) with semicircular ends (each with diameter m). Using , find the total track area.