Area of Composite Figures Word Problems
Concept
The area of composite shapes is the area that is covered by any composite shape. The composite shape is a shape in which few polygons are put together to form a required shape. These shapes or figures can be made up of a combination of triangles, squares, and quadrilaterals, etc. Divide a composite shape into basic shapes like square, triangle, rectangle, hexagon, etc. to determine the area of composite shapes.
Rules
1. Read the word problem and decompose the composite figure into simpler shapes of which you can find the area.
2. Write down the area formulas of the simpler shapes.
3. Substitute the given values into the formulas.
4. Add or subtract the areas of the simple shapes as needed and state the correct square units.
Example
A hotel is building a heart-shaped pool. Find the area of the pool. Use 3.14 for π.
Solution
The area is composed of a square and two semicircles (one whole circle).
Area of the pool = Area of a circle + Area of a square
= πr2 + s2
= 3.14 (18.25 m)2 + (36.5 m)2
= 1045.81 m2 + 1332.25 m2
= 2378.1 m2
Practice Area of Composite Figures Word Problems
Practice Problem 1
Tommy needs to paint a wall except for the window. The dimensions are shown below. How many cans of paint does he need if 1 can of paint can cover 1 m2?
Practice Problem 2
Annie is making a door for her dollhouse from a paper. How much paper does she need? Dimensions of the door are shown below. Use 3.14 for π. Round to the nearest tenth.
Practice Problem 3
A photo frame is shown below with its dimensions. If the glass portion only covers the picture inside of the frame, what is the area of a piece of replacement glass?
Composite figure – a figure created by adding two or more shapes.
Area – the space occupied by a flat shape or the surface of an object.