Introduction
Similarity in Two- and Three-Dimensional Figures

Three-dimensional prisms

If two figures are similar, the ratio of their corresponding links will be the same. In this topic, you will learn to solve problems involving similar two-dimensional and three-dimensional figures. You will explore the significance of the scale factor of similar figures in solving problems involving area and volume. In addition, you will learn how changing one or more dimensions of a figure can affect its area or volume. Of course, the reverse is also true: if you change the volume of a figure, it will affect the dimensions of that figure.

Essential Questions

 

Warm-Up

Warm-up iconBefore beginning your exploration of similar two-dimension and three-dimensional figures, check your knowledge of earlier concepts in geometry. Can you calculate the perimeter and area of the figures below? Hover your mouse over each rectangle below to reveal the correct answer to each question.

Rectangle 1

Rectangle with lenght of 5 and width of 2

 

Q. What is the perimeter of the rectangle? A. Perimeter = 5 + 2 + 5 +2 = 14

Q. What is the area of the rectangle? A. Area = 5 x 2 = 10

 

Rectangle 2

What are the dimensions of the rectangle if you triple the length and width of Rectangle 1? Sketch the new rectangle and include its dimensions. Then, hover your mouse over the image below to view the correct dimensions.

Rectangle with a length of 15 and width of 6

 

Q. What is the perimeter of the rectangle? A. Perimeter = 15 + 6 + 15 + 6 = 42

Q. What is the area of the rectangle? A. Area = 15 x 6 = 90