Describe what it means to enlarge or reduce a shape.
Explain why we do not use a unit when writing the value of a scale factor.
Triangle ABC has been enlarged to triangle A'B'C'.
Calculate the scale factor.
Triangle A'B'C' has been reduced to form a smaller triangle ABC.
Calculate the scale factor.
Triangle ABC has been enlarged to triangle A'B'C'.
Calculate the scale factor.
Is quadrilateral A'B'C'D' an enlargement of quadrilateral ABCD? Explain your answer.
Quadrilateral A'B'C'D' is an enlargement of quadrilateral ABCD.
Calculate the scale factor.
For each pair of similar figures and given scale factor:
Determine the reduction factor.
Determine the enlargement factor.
The two figures to the right are similar.
State the reduction factor as a fraction.
Hence, find the value of m.
The two figures to the right are similar.
State the enlargement factor as a fraction.
Hence, find the value of x.
Quadrilateral ACBD is to be enlarged.
For each enlargement factor below, determine the new position of point A on the number line:
Enlargement factor of 3.
Enlargement factor of \dfrac{1}{3}.
The dimensions of the triangle shown are enlarged using a scale factor of 3.1.
Determine the new length of:
AB
BC
CA
The dimensions of the triangle shown are reduced using a scale factor of 0.92.
Determine the new length of:
AB
BC
CA
An equilateral triangle of side length 6\text{ cm} is to be enlarged by a factor of 5.
What will be the side length in the resulting triangle?
What will be the size of each angle in the resulting triangle?
In the following figure, the scale factor used to enlarge the smaller quadrilateral is 4.5.
Find the length of FG.
Glass in the shape of a circle has a radius of 12\text{ cm}. When it is blown, the radius becomes 48\text{ cm}.
What is the enlargement factor?
Determine the enlargement factor for the two circles in the diagram:
These two Christmas trees are similar:
Determine the reduction factor.
Hence, find x.
A rectangle is 8\text{ cm} long and 6\text{ cm} wide. If its dimensions are enlarged such that its length is now 28\text{ cm}, what is its new width?
If a scale factor of \dfrac{2}{3} is applied to a shape, will the new shape be larger or smaller than the original?
If an image is enlarged by 250\%, what is the scale factor as a decimal value?
A square with area 4\text{ cm}^{2} has its side lengths enlarged by a factor of 3.
Determine the side length of the original square.
Calculate the area of the new square.
By what factor has the area been enlarged?
The area of a square is 30\text{ cm}^{2}. Its side length is enlarged by a scale factor of 3.
Calculate the area of the new square.
Consider the two given triangles drawn on a 1\text{ cm}^{2} grid:
Calculate the scale factor used to enlarge the small triangle.
Calculate the scale factor used to reduce the large triangle.
Find the area of the small triangle.
Find the area of the large triangle.
State the enlargement factor from the area of the small triangle to the area of the large triangle.
The corresponding sides of the following similar figures are in the ratio 7:3:
State the length scale factor from the left figure to the right figure.
State the area scale factor from the left figure to the right figure.
State the area scale factor for each of the following linear scale factors:
10
\dfrac{3}{10}
\dfrac{1}{3}
Find the value of x for each pair of similar figures:
The corresponding sides of two similar triangles are 8\text{ cm} and 40\text{ cm}.
If the area of the smaller triangle is 24\text{ cm}^{2}, find A, the area of the larger triangle.
A square of side length 6\text{ cm} is enlarged using the scale factor 3.
Find the area of the enlarged square.
If the diameter of a circle is tripled, calculate the scale factor applied to the area of the circle.
Consider the formula for the area of a triangle, A = \dfrac{1}{2} b h.
If the value of b increases by a factor of 2 and the value of h is reduced by a factor of 2, what is overall effect does this have on A?
Consider the formula for the area of a circle, A = \pi r^{2}.
If the value of r were to triple, what overall effect would this have on A?
The bases of two similar rectangular prisms are: 30\text{ cm} by 45\text{ cm}; and 6\text{ cm} by 9\text{ cm}.
State the length scale factor.
State the surface area scale factor.
Find the surface area of the smaller prism, knowing that the surface area of the larger prism is 4425\text{ cm}^{2}.
A triangle has side lengths of 7 \text{ cm}, 10\text{ cm} and 16\text{ cm}. A similar triangle to it has 9 times the area of the first triangle.
State the length scale factor between the two triangles.
List the side lengths of the second triangle.
Describe the relationship between the perimeters of the two triangles.
Consider two similar parallelograms with matching sides in the ratio 6:8.
Calculate the area of the larger parallelogram, if the area of the smaller parallelogram is 72\text{ cm}^{2}.
Find the length of the base of the smaller parallelogram, if the length of the base of the larger parallelogram is 12\text{ cm}.
Two pentagonal prisms are similar. The areas of their cross-sectional faces are given.
Calculate the surface area scale factor from Figure I to Figure II.
State the length scale factor from Figure I to Figure II.
Calculate the height of Figure II, if Figure I is 13 \text{ mm} high.
Two similar cones have bases with radius 7\text{ cm} and 28\text{ cm} respectively.
State the scale factor of the height of the smaller cone to the height of the larger cone.
State the scale factor of the volume of the smaller cone to the volume of the larger cone.
Calculate the volume of the larger cone, if the volume of the smaller cone is 852\text{ cm}^{3}.
The radii of two spherical balloons are 12\text{ cm} and 6\text{ cm} respectively.
Determine the ratio of the radii of the circles.
State the ratio of their surface areas.
State the ratio of their volumes.
Calculate the ratio of the balloon volumes, if half the air is released from the smaller balloon.
The surface areas of two similar triangular prisms are in the ratio 64:49.
State the scale factor of their sides.
State the scale factor of their volumes.
The volume of two similar crates are in the ratio 1331:125.
State the ratio of their sides.
State the ratio of their surface areas.
Consider the two similar trapezoidal prisms:
State the length scale factor, from the smaller prism to the larger prism.
State the volume scale factor, from the smaller prism to the larger prism.
The dimensions of a cement slab are l the length, w the width and h the thickness. If these dimensions are tripled describe the effect on:
The surface area of the cement slab.
The volume of the cement slab.
Consider these two rectangular prisms:
Are the two rectangular prisms similar?
Find the length scale factor from the smaller prism to the larger.
Find the surface area scale factor from the smaller prism to the larger.
Find the volume scale factor from the smaller prism to the larger.
Find the volume scale factor from the smaller prism to the larger, if the measurements of the smaller prism are doubled.
William recorded a video on his camera. When viewing it on the camera screen, the video appeared in a width to length ratio of 4:3 respectively.
When he uploaded to his computer, everything appeared wider in the video. Which of the following could be the ratio in which the video is shown on his computer?
8:6
20:12
16:12
8:9
10:7.5
A circular oil spill has a radius of 20\text{ m}. In a photo taken of the oil spill, the circle is reduced by a factor of 500.
Determine the radius of the circular oil spill in the photo. Round your answer to the nearest centimetre.
Mae wants to insert a picture into a document. She enlarges it by a factor of 12 but it becomes too blurry, so she reduces the resulting picture by a scale factor of 4.
Calculate the overall scale factor from the original to the final size.
A piece of sports tape in the shape of a rectangle measures 6\text{ cm} in width and 10\text{ cm} in length (when not stretched). When applied to Sophia’s shoulder, it is stretched so that it covers a rectangular area measuring 12\text{ cm} wide by 20\text{ cm} long.
When not stretched, calculate the area of the tape.
When stretched, calculate the area of the tape.
By what scale factor are the lengths of the rectangular tape enlarged when stretched?
By what scale factor is the area of the rectangular tape enlarged when stretched?
Susana has two teddy bears that have the same shape but are different sizes. The length of the first teddy bear is 15\text{ cm}, while the length of the second teddy bear is 75\text{ cm}.
Find the length scale factor.
Find the surface area scale factor.
If the smaller bear needs 375\text{ cm}^{2} to be covered with 'fake fur', find the amount of 'fake fur' needed for the bigger bear.
Valentina was making a trial birthday cake for her son. The trial cake dimensions are 10\text{ cm} for the length, 7\text{ cm} for the width and 3\text{ cm} for the height. The actual cake has dimensions 20\text{ cm} for the length, 14\text{ cm} for the width and 6\text{ cm} for the height.
State the ratio of the dimensions of the trial cake to those of the actual cake.
Hence, deduce the ratio of the volume of the trial cake to that of the actual cake.
To make the actual cake, by what number must Valentina multiply each quantity of ingredients?
Consider two similar rectangular ceilings: the first with dimensions 5\text{ m} by 4\text{ m}, and the second with dimensions 20\text{ m} by 16\text{ m}.
State the length scale factor from the small ceiling to the large ceiling.
State the area scale factor from the small ceiling to the large ceiling.
The smaller ceiling took 1.5\text{ L} of paint to cover it. Calculate the number of litres of paint required to paint the second ceiling.
The model of Eiffel tower is made with a ratio 1:6480.
Calculate the height of the model, in centimetres, if the height of Eiffel tower is 324\text{ m}.
State the ratio of the surface area of the model to the surface area of Eiffel tower.
The ratio of the length of a model car to a real car is 1:20.
State the ratio of surface area of the model car to the real car.
State the ratio of the volume of the model car to the real car.
Calculate how many litres of paint are needed to paint the real car, if 18 \text{ mL} are needed to paint the model car.
Find the capacity of the model car fuel tank, in mL, if the real car fuel tank holds 48 \text{ L}.
A beehive consists of regular hexagonal cells with side length 3.2\text{ mm} and depth of 3.8\text{ mm}. A plastic container is built which is modelled on these hexagonal cells, with a side length of 6.4\text{ cm}.
State the ratio of the length of the side of the beehive to the length side of the modelled storage unit.
State the ratio of the surface area of the side of the beehive to the surface area side of the modelled storage unit.
State the ratio of the volume of the beehive to the volume of the modelled storage unit.
A rectangular billboard has a length of 1.2\text{ m}. The corresponding length on a similar rectangular computer screen is 20\text{ cm}.
State the length scale factor from the computer screen to the billboard.
State the area scale factor from the computer screen to the billboard.
Calculate the area of a maximised image on the screen, if the area on the billboard is 86.4\text{ m}^{2}.