Worksheet: Ratios of Geometric Figures

In this worksheet, we will practice writing and simplifying ratios and using that to solve problems in geometric context.

Q1:

Find the ratio between the lengths 120cm and 3.2 m in its simplest form.

  • A803
  • B154
  • C380
  • D38
  • E83

Q2:

Find, in the simplest form, the ratio between the circumference of a circle whose radius is 7 cm and the perimeter of a square whose side length is 4.5 cm, where 𝜋=227.

  • A922
  • B229
  • C114
  • D411

Q3:

In a given rectangle, the length is four times the width. If the length is 40 cm, express the ratio between the rectangle’s perimeter and length in its simplest form.

  • A110
  • B101
  • C507
  • D52
  • E25

Q4:

Using the figures, determine the ratio between the area of triangle 𝐴𝐵𝐶 and the area of square 𝑋𝑌𝑍𝐿. Give your answer in its simplest form.

  • A41
  • B45
  • C85
  • D81

Q5:

In the figure below, what is the ratio between the green parts and red parts in its simplest form?

  • A23
  • B21
  • C12
  • D32

Q6:

Determine the ratio between the quantities 242802.2dmcmm in the simplest form.

  • A121411
  • B1201114
  • C1201411
  • D121114

Q7:

Express the following ratio in its simplest form: 18675LmL.

  • A541
  • B527
  • C154
  • D275
  • E5216

Q8:

Express the ratio 4.72,35018.8kmmkm in its simplest form.

  • A128
  • B218
  • C821
  • D812

Q9:

A square has side length 12 cm and a rectangle has sides of length 20 cm and 6 cm. What is the ratio between the perimeter of the rectangle and that of the square in its simplest form?

  • A1213
  • B56
  • C65
  • D52
  • E1312

Q10:

If the side length of a square is equal to the side length of an equilateral triangle, what is the ratio of the perimeter of the square to the perimeter of the equaliteral triangle?

  • A13
  • B43
  • C41
  • D34

Q11:

Square A has a side length of 6𝑥 cm. Square B has a side length of 7𝑥 cm. What is the ratio of the areas of squares A and B in its simplest form?

  • A76
  • B3649
  • C4936
  • D67

Q12:

Given that the area of a triangle is 52 cm2, and its base length is 13 cm, determine the ratio between its base length and its height.

  • A136
  • B813
  • C138
  • D613

Q13:

The area of a rectangle is 210 cm2, and its width is 10 cm. What is the ratio between the length and perimeter of the rectangle in its simplest form?

  • A1021
  • B2110
  • C6221
  • D531
  • E2162

Q14:

A triangle has side lengths 3 cm, 4 cm, and 5 cm. A rhombus has side length 0.16 m. Express the ratio of the perimeters of the triangle and the rhombus in its simplest form.

  • A43
  • B34
  • C316
  • D163

Q15:

The length of the diagonal in a square is 10 cm. A parallelogram has a base length of 13 cm and perpendicular height of 4 cm. What is the ratio between the areas of the square and the parallelogram in its simplest form?

  • A2513
  • B1325
  • C2625
  • D2526

Q16:

A parallelogram has a base length of 90 mm and corresponding height of 70 mm. A rhombus has diagonal lengths of 7 cm and 6.2 cm. Find the ratio of the area of the parallelogram to that of the rhombus.

  • A3145
  • B3190
  • C4531
  • D9031

Q17:

A square has a perimeter of 2.4 m. A rectangle has a width of 12 cm, and its length exceeds the side length of the square by 16 cm. Express the ratio of the area of the square to the area of the rectangle in its simplest form.

  • A15
  • B51
  • C7519
  • D1975

Q18:

Find the ratio between the perimeter of the rhombus and the circumference of the circle in its simplest form using 𝜋=227.

  • A144
  • B2511
  • C122
  • D5011

Q19:

A piece of wire, which is 120 cm, was divided into two parts with a ratio of 114. A circle was shaped from the long part, and a square was shaped from the short one. Determine the ratio between the area of the square and that of the circle in its simplest form. 𝜋=227.

  • A411
  • B778
  • C877
  • D114

Q20:

The side length of a square is 2 cm. A rectangle has length 7 cm and width 5 cm. Find the ratio between the perimeter of the square and the perimeter of the rectangle in its simplest form.

  • A435
  • B23
  • C16
  • D13

Q21:

The side length of a square is 4 cm. A rectangle has length 4 cm and width 3 cm. Find the ratio between the area of the square and the area of the rectangle in its simplest form.

  • A13
  • B43
  • C11
  • D87

Q22:

Write this ratio in its simplest form: The ratio of the circumference of a circle to its diameter.

  • A12𝜋
  • B𝜋1
  • C2𝜋1
  • D1𝜋

Q23:

Write this ratio in its simplest form: The ratio of the side length of a square to its perimeter.

  • A14
  • B31
  • C41
  • D13

Q24:

The sum of the dimensions of a rectangular prism is 54 cm and the ratio among the lengths of its dimensions is 567. Find its volume.

Q25:

The sum of lengths of the edges of a cuboid is 100 cm. If the base dimensions are in the ratio 32, and its height 1 dm, find the total surface area and volume of the cuboid.

  • Atotal surface area 324.48 cm2, volume 138.24 cm3
  • Btotal surface area 300 cm2, volume 540 cm3
  • Ctotal surface area 154.67 cm2, volume 106.67 cm3
  • Dtotal surface area 408 cm2, volume 540 cm3

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