12 multiple-choice questions, progressively harder.
A simple polygon of area 777 square units has a similar image with length scale factor 444. What is the image area?
Solution
Correct answer: B
Area uses the square of the length factor.
Similar polygons have original perimeter 454545 cm. The length scale factor taking the original to its image is 0.60.60.6. Which choice gives the image perimeter and its area as a percentage of the original area?
272727 cm
60%60\%60% of the original area
16.216.216.2 cm
36%36\%36% of the original area
757575 cm
Correct answer: D
Perimeter uses the length factor once, while area uses its square.
The image has 36%36\%36% of the original area.
The ratio of corresponding lengths in two similar polygons is 5:85:85:8, in that order. What is their area ratio in the same order?
Correct answer: A
Square both terms without reversing their order.
A similar image has 1/161/161/16 of the original area. What positive number multiplies an original length to give its corresponding image length?
Correct answer: C
Similarity permits the positive square root of the area factor.
An original side of 181818 mm corresponds to a 272727 mm image side in similar polygons. What is the image-over-original area factor?
Find the image-over-original length factor, then square it.
Two similar images of one polygon use length factors 1 and 2, respectively. Which statement is guaranteed?
Both images are congruent to the original.
The second has twice the original area.
The first image has twice the original area.
The second has four times the original area.
The first image is congruent to the original.
Length factor 111 preserves both shape and size, so the first image is congruent to the original. The second image uses squared area factor
Thus the second has four times the original area.
A polygon has area measured in square millimeters. It is carried to a similar image with dimensionless length factor 333. Which unit belongs to the image area after multiplying by the squared factor?
Squaring the length scale factor changes the number of square units, not the unit itself. The multiplier is dimensionless.
The image area is still measured in square millimeters.
A triangle has base 141414 cm and perpendicular height 999 cm. A similar image has length factor 222. What is the image area?
The original area is half the base times the height.
A polygon is partitioned into nonoverlapping triangles. Under one similarity, which fact allows their image areas to be added to obtain the whole image area?
A similarity carries every cut and piece to the image. Coverage and nonoverlap are preserved, so the area-addition postulate applies.
Similar figures have original area 8 m28\text{ m}^28 m2 and image area 18 m218\text{ m}^218 m2. What number multiplies an original length to give its corresponding image length?
Use image area over original area, then take the positive square root.
Similar triangles have original area 64 cm264\text{ cm}^264 cm2 and image area 16 cm216\text{ cm}^216 cm2. An original side is 121212 cm. How long is its corresponding image side?
The area factor is 1/41/41/4, so the length factor is 1/21/21/2.
Only the areas of two polygons are known. What further information is needed before their area ratio can determine corresponding length ratios?
The square-root rule for corresponding lengths assumes similarity. Positive areas and matching square units make an area ratio meaningful but do not supply a matching shape.
Reset this practice set?
This clears every answer you have given and starts the set again from question 1.