11. Modeling in Two and Three dimensions

11.01 Area and perimeter

11.02 Prisms and cylinders

11.03 Pyramids and cones

11.05 Similarity in 2D and 3D figures

United States of America

Grades 9-12

11.05 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

2 min

Consider the two similar rectangles shown in the figure.

Easy

2 min

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

1 min

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

Easy

1 min

Outcomes

HSG.GMD.A.3

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

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