Area and Similarity: Practice Level 2 | Geometry

Level 2 · Intermediate 0 / 12 answered

Question 1 of 12

1

A polygon with area $120\text{ cm}^2$ is mapped to a similar image with length factor $0.4$ . What is the image area?

Answer choices for question 1 A $48\text{ cm}^2$ B $300\text{ cm}^2$ C $19.2\text{ cm}^2$ D $192\text{ cm}^2$
2

A side of $9$ cm corresponds to a $15$ cm image side in similar polygons. The original area is $81\text{ cm}^2$ . What is the image area?

Answer choices for question 2 A $225\text{ cm}^2$ B $135\text{ cm}^2$ C $48.6\text{ cm}^2$ D $729\text{ cm}^2$
3

Similar triangles have original area $98\text{ cm}^2$ and image area $200\text{ cm}^2$ . The original altitude is $21$ cm. What is the corresponding image altitude?

Answer choices for question 3 A $42$ cm B $210/49$ cm C $300/7$ cm D $30$ cm
4

Similar polygons have original perimeter $32$ cm and image perimeter $48$ cm. The original area is $64\text{ cm}^2$ . What is the image area?

Answer choices for question 4 A $96\text{ cm}^2$ B $144\text{ cm}^2$ C $256\text{ cm}^2$ D $128/3\text{ cm}^2$
5

A similar image has length factor $2$ and $81\text{ cm}^2$ more area than its original. What is the original area?

Answer choices for question 5 A $40.5\text{ cm}^2$ B $20.25\text{ cm}^2$ C $81\text{ cm}^2$ D $27\text{ cm}^2$
6

In nondegenerate triangle ABC, D is between A and B, E is between A and C, and DE is parallel to BC. The ratio AD to AB is $2:7$ . What fraction of the area of ABC lies outside triangle ADE?

Answer choices for question 6 A $4/49$ B $5/7$ C $45/49$ D $25/49$
7

Two images of the same polygon of area $50$ square units use length factors $3$ and $4$ . How much greater is the second image area?

Answer choices for question 7 A $350$ square units B $50$ square units C $150$ square units D $700$ square units
8

A rectangle has perimeter $40$ cm and area $96\text{ cm}^2$ . A similar rectangle has area $150\text{ cm}^2$ . What is its perimeter?

Answer choices for question 8 A $62.5$ cm B $50$ cm C $32$ cm D $100$ cm
9

A triangle of area $32\text{ cm}^2$ has an altitude of $6$ cm. Its similar image has area $72\text{ cm}^2$ . What is the corresponding image altitude?

Answer choices for question 9 A $13.5$ cm B $4$ cm C $9$ cm D $18$ cm
10

A polygon is enlarged to a similar image whose area is three times the original area. What is the positive length scale factor?

Answer choices for question 10 A $3$ B $9$ C $3/2$ D $\sqrt3$
11

A polygon of area $90\text{ cm}^2$ contains a marked triangular part of area $18\text{ cm}^2$ . A similarity carries the polygon and the part to an image of total area $360\text{ cm}^2$ . What is the marked image area?

Answer choices for question 11 A $36\text{ cm}^2$ B $72\text{ cm}^2$ C $288\text{ cm}^2$ D $4.5\text{ cm}^2$
12

A $5$ cm by $12$ cm rectangle and a $10$ cm by $24$ cm rectangle are compared, with the second rotated on the page. What is the second-to-first area ratio?

Answer choices for question 12 A $4:1$ B $2:1$ C $1:4$ D $7:2$