Digits, Grade 7, Volume 1, Homework Helper

4-5: Area of Composite Figures

Key Concept

A composite figure is the combination of two or more shapes. Often you can decompose a composite figure more than one way.

A composite figure formed by placing a square with side length 3 feet and area 9 square feet against a rectangle with length 5 feet, height 6 feet, and area 30 square feet.

Area of figure = area of square + area of rectangle

table with 2 rows and 1 column , row1 column 1 , equals 9 plus 30 , row2 column 1 , equals 39 , end table

The area of the figure is 39 ft2.

Part 1

Example Finding Areas of Polygons

The polygon is a floor plan for a new music area in a school. What is the area of the polygon?

A polygon with five sides. Sides of length 4 meters and 11 meters meet the side of length 9 meters at right angles. A fourth side of length 5 meters forms a right angle with the 11-meter side.

Solution

Method 1 Decompose the polygon into a square, a right triangle, and a rectangle.

Area of square: 42 = 16, or 16 m2

Area of a right triangle: 1 half , middle dot 7 middle dot 4 equals 14 comma or 14 , m super 2 end super

Area of rectangle: 11 · 5 = 55, or 55 m2


End ofPage 147

Table of Contents

Digits, Grade 7, Volume 1, Homework Helper Unit A: Number and Operations Unit B: Expressions, Equations, and Relationships Unit C: Measurement and Geometry Unit D: Proportionality English/Spanish Glossary Formulas Math Symbols Formulas Measures Properties