9. Modeling in Two and Three dimensions

9.01 Area and perimeter

9.02 Cross sections and revolutions of solids

9.03 Prisms and cylinders

9.04 Pyramids and cones

9.06 Geometric modeling (M)

9.07 Similarity in 2D and 3D figures

United States of America

Grades 9-12

9.07 Similarity in 2D and 3D figures

Adaptive

Worksheet

Interactive practice questions

Consider the two given triangles.

Two triangles displayed on a grid. The smaller triangle on the left has vertices labeled A, B, and C, with vertex C serving as the apex of triangle ABC, and vertices A and B located on the base. Vertex A is 4 units to the left of vertex B. Vertex C is 3 units above the base AB. The larger triangle on the right has vertices labeled D, E, and F, with vertex F as the apex of triangle DEF, and vertices D and E positioned on the base. Vertex D is 8 units to the left of vertex E. Vertex F is 6 units above base DE Triangle DEF is an enlarged version of triangle ABC.

a

What scale factor is used to enlarge the small triangle?

b

What scale factor is used to reduce the large triangle?

c

What is the area of the small triangle?

d

What is the area of the large triangle?

e

What is the enlargement factor for the area of the small triangle?

Easy

2min

Consider the two similar rectangles shown in the figure.

Easy

2min

The corresponding sides of two similar triangles are $8$8 cm and $40$40 cm. If the area of the smaller triangle is $24$24 cm². Find $A$A the area of the larger triangle.

Easy

1min

A square of side length $6$6 cm is enlarged using the scale factor $3$3. Find the area of the enlarged square.

Easy

1min

Outcomes

G.GMD.A.3

Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

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