Mathematics
Grade 10
15 min
Areas of similar figures
Areas of similar figures
What you'll learn
- Identify the dividend, divisor, and quotient in division word problems with 80% accuracy.
- Solve at least 3 out of 4 word problems involving division of 2-digit and 3-digit numbers by 2-digit numbers using a strategy like long division or partial quotients.
- Explain the steps taken to solve a division word problem to a partner, using mathematical vocabulary (dividend, divisor, quotient, remainder) in their explanation.
- Apply division to solve real-world problems involving equal sharing and grouping with at least 75% accuracy.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
State the relationship between the ratio of similarity and the ratio of areas for two similar figures.
Calculate the ratio of areas given the ratio of corresponding side lengths.
Calculate the ratio of corresponding side lengths given the ratio of areas.
Solve for a missing area of a figure given a similar figure with a known area and corresponding side lengths.
Solve for a missing side length of a figure given its area and a similar figure with a known area and corresponding side length.
Apply the area ratio theorem to solve real-world problems involving scaling.
Ever wonder how an architect can be sure a building will be sound just by looking at a small blueprint? 📐 It's all about scaling, and the math is more powerful than you think!
In this tut...
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Key Concepts & Vocabulary
TermDefinitionExample
Similar FiguresTwo geometric figures are similar if they have the same shape but not necessarily the same size. This means their corresponding angles are congruent (equal) and the ratios of their corresponding side lengths are equal.A 3cm x 4cm rectangle is similar to a 6cm x 8cm rectangle because all angles are 90° and the sides are in a 1:2 ratio.
Ratio of Similarity (or Scale Factor)The constant ratio of the lengths of any two corresponding sides of similar figures. It is often denoted by the variable 'k'.If Triangle ABC is similar to Triangle XYZ and side AB = 5 and corresponding side XY = 15, the ratio of similarity is 5/15 = 1/3.
Corresponding SidesSides that are in the same relative position in two similar figures.In two similar triangles, the side o...
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Core Formulas
Ratio of Perimeters Theorem
If the ratio of similarity of two similar figures is a : b, then the ratio of their perimeters is also a : b.
Use this rule to relate the side lengths of similar figures directly to their perimeters. If you know the scale factor, you know the perimeter ratio.
Ratio of Areas Theorem
If the ratio of similarity of two similar figures is a : b, then the ratio of their areas is a^2 : b^2.
This is the core rule for this lesson. To find the ratio of areas, you must square the ratio of the corresponding sides. This works for all similar polygons, circles, and other 2D figures.
Finding an Unknown Area
(Side_1 / Side_2)^2 = Area_1 / Area_2
This formula is a direct application of the Ratio of Areas Theorem. Set up a proportion with the square of the...
4 more steps in this tutorial
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Challenging
In ΔABC, a line segment DE is drawn parallel to BC, with D on AB and E on AC. If the area of ΔADE is one-fourth the area of ΔABC, what is the ratio of the length of AD to the length of DB?
A.1 : 2
B.1 : 1
C.1 : 4
D.1 : 3
Challenging
A circular pizza with a 20 cm diameter costs $16.00. Assuming the cost is directly proportional to the area, what should be the price of a similar pizza with a 30 cm diameter?
A.$36.00
B.$24.00
C.$32.00
D.$40.00
Challenging
The areas of two similar polygons are `25x²` and `49x²`. The length of a side on the larger polygon is `14y`. What is the length of the corresponding side on the smaller polygon in terms of `y`?
A.7y
B.5y
C.10y
D.25y/7
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Frequently asked questions
What grade level is "Areas of similar figures"?
Areas of similar figures is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Areas of similar figures?
You'll be able to: Identify the dividend, divisor, and quotient in division word problems with 80% accuracy; Solve at least 3 out of 4 word problems involving division of 2-digit and 3-digit numbers by 2-digit numbers using a strategy like long….
Is "Areas 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 Areas of similar figures?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.