7th Grade - Area of Composite Figures

Introduction

• Composite figures are obtained by combining two or more geometric figures.
• For example, the composite figure shown below is obtained by combining a rectangle and a triangle.

 

Area of Composite Figures

• The area of a composite figure is the surface measurement or square units it covers.
• The area of a composite figure can be calculated in the steps mentioned below.
  1. Decomposing (breaking apart) the composite figure into basic geometric shapes such as rectangles, squares, triangles, circles, etc.
  2. Adding/subtracting the area of each shape
• The area of some of the standard shapes is mentioned below.

 

 

 

Click here to learn more about triangles: 

 

Click here to learn more about circles & semi-circles: 

Click here to learn more about parallelograms: 

Click here to learn more about trapeziums: 

Perimeter of Composite Figures

• The perimeter of a composite figure is the measure of the length of its boundary.
• For example, the perimeter of the composite figure shown below is the sum of the three sides of a rectangle and the circumference of the semi-circle.

 

Solved Examples

Question 1: Find the area of the composite figure shown below.

Solution: The given composite figure can be represented as the combination of a rectangle and a triangle, as shown below.

Area of composite figure = Area of rectangle + Area of triangle

$=\left(5\times 4\right)+\frac{1}{2}\times 5\times 5$

$=20+12.5$

$=32.5 i{n}^2$

 

Question 2: Find the perimeter of the composite figure shown below.

Solution: The given composite figure can be represented as shown below.

Area of composite figure = Area of the rectangle - Area of the semi-circle

$=\left(7\times 11\right)-\frac{\mathrm{\pi }{\left(3.5\right)}^2}{2}$

$=77-\frac{3.14\times 12.25}{2}$

$=77-19.23$

$=57.77 m^2$

Cheat Sheet

• The area of a composite figure is calculated by dividing the composite figure into basic figures and then adding or subtracting the respective regions.
• The perimeter of a composite figure is the measure of the length of its boundary.

Blunder Areas

• It is important to identify the dimensions such as the base and the height, the length and the width of each shape. Then analyze whether the individual areas of the composite figure need to be added or subtracted.
• Note that the perimeter of a composite figure is not equal to the perimeter of individual basic figures.