6. Similar Figures and Scale factors

6.01 Conditions for similarity

6.02 Scale factors in similar figures

6.025 Scale ratios

6.03 Applications of scale factor to area, surface area and volume

Year 11

6.03 Applications of scale factor to area, surface area and volume

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

A square with area $4$4 cm² has its side lengths enlarged by a factor of $3$3.

Easy

1min

A triangle has side lengths of $7$7 $cm$ , $10$10 $cm$ and $16$16 $cm$ . A similar triangle to it has $9$9 times the area of the first triangle.

Easy

2min

Find the value of $x$x in each of the following cases:

Easy

3min

Outcomes

1.2.3.4

obtain a scale factor and use it to solve scaling problems involving the calculation of the areas of similar figures, including the use of shadow sticks, calculating the height of trees, use of a clinometer

1.2.3.5

obtain a scale factor and use it to solve scaling problems involving the calculation of surface areas and volumes of similar solids

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