Mathematics
Grade 10
15 min
Area and perimeter of similar figures
Area and perimeter of similar figures
What you'll learn
- Identify the equivalent fraction and decimal for at least 8 out of 10 given percentages.
- Convert at least 7 out of 10 given fractions (with denominators of 2, 4, 5, 10, 20, 25, 50, and 100) into their equivalent percentages and decimals.
- Solve 3 out of 4 word problems that require converting between percents, fractions, and decimals to find a solution.
- Explain, in their own words, the relationship between percents, fractions, and decimals, using at least 2 examples.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Define the similarity ratio (scale factor) for two similar figures.
Explain the relationship between the similarity ratio and the ratio of perimeters.
Explain the relationship between the similarity ratio and the ratio of areas.
Calculate the perimeter of a similar figure using the ratio of perimeters.
Calculate the area of a similar figure using the ratio of areas.
Determine the similarity ratio or an unknown side length when given the areas or perimeters of two similar figures.
Apply these concepts to solve multi-step problems.
Ever wonder how a tiny blueprint accurately represents a massive skyscraper, or how a small photo can be enlarged for a billboard without distortion? 🏙️
This tutorial explores the powerful mathematical relationship between sim...
2
Key Concepts & Vocabulary
TermDefinitionExample
Similar FiguresTwo geometric figures that have the exact same shape, but may have different sizes. Their corresponding angles are congruent, and the ratio of their corresponding side lengths is constant.A 3-4-5 right triangle and a 6-8-10 right triangle are similar. All angles are the same, and each side of the second triangle is twice the length of the corresponding side of the first.
Similarity Ratio (or Scale Factor)The constant ratio of the lengths of corresponding sides of two similar figures. It is often denoted by the variable 'k'.If Triangle ABC is similar to Triangle XYZ, and side AB = 5 cm while corresponding side XY = 15 cm, the similarity ratio from ABC to XYZ is 15/5 = 3, or 3:1.
Corresponding Sides/AnglesSides or angles that are in the same re...
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Core Formulas
Ratio of Perimeters Theorem
If the similarity ratio of two similar figures is \( \frac{a}{b} \), then the ratio of their perimeters is also \( \frac{a}{b} \). \( \frac{\text{Perimeter}_1}{\text{Perimeter}_2} = \frac{\text{side}_1}{\text{side}_2} = \frac{a}{b} \)
Use this rule to find an unknown perimeter when you know the similarity ratio and the other figure's perimeter. The relationship is linear.
Ratio of Areas Theorem
If the similarity ratio of two similar figures is \( \frac{a}{b} \), then the ratio of their areas is \( (\frac{a}{b})^2 = \frac{a^2}{b^2} \). \( \frac{\text{Area}_1}{\text{Area}_2} = (\frac{\text{side}_1}{\text{side}_2})^2 = \frac{a^2}{b^2} \)
Use this rule to find an unknown area. Remember that since area is a two-dimensional measurement (e.g., cm²),...
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Challenging
A company makes two similar triangular logos. The cost of the material is directly proportional to the area. The smaller logo has a base of 6 cm and costs $1.80 to produce. The larger logo has a corresponding base of 15 cm. What is the cost to produce the larger logo?
A.$4.50
B.$7.50
C.$11.25
D.$28.13
Challenging
Two similar polygons have areas of A₁ = (x + 10) cm² and A₂ = (x + 70) cm². Their corresponding side lengths are 4 cm and 8 cm. Find the area of the larger polygon, A₂.
A.80 cm²
B.60 cm²
C.100 cm²
D.70 cm²
Challenging
A large square with side length 'S' contains a smaller, similar square with side length 's' such that the area of the large square is 9 times the area of the small square. The region between the two squares is shaded. If the perimeter of the shaded region is 80 units, what is the side length 'S' of the large square?
A.12
B.15
C.20
D.30
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Frequently asked questions
What grade level is "Area and perimeter of similar figures"?
Area and perimeter of similar figures is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Area and perimeter of similar figures?
You'll be able to: Identify the equivalent fraction and decimal for at least 8 out of 10 given percentages; Convert at least 7 out of 10 given fractions (with denominators of 2, 4, 5, 10, 20, 25, 50, and 100) into their equivalent percentages and….
Is "Area and perimeter of similar figures" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Area and perimeter of similar figures?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.