Mathematics
Grade 10
15 min
Area of compound figures
Area of compound figures
What you'll learn
- Identify the key information (total, percent, part) in percent word problems with 80% accuracy.
- Solve percent of a number word problems using at least one strategy (e.g., converting percent to decimal, using proportions) and show their work correctly in at least 4 out of 5 problems.
- Explain their reasoning for solving a percent word problem in their own words, demonstrating understanding of the relationship between the percent, the whole, and the part, in at least 3 out of 4 attempts.
- Apply their knowledge of percentages to solve real-world word problems involving discounts, sales tax, and tips with 75% accuracy.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Decompose a compound figure into simpler, non-overlapping geometric shapes.
Select and apply the appropriate area formulas for various polygons and circles.
Calculate the total area of a compound figure using both the addition and subtraction methods.
Use the Pythagorean theorem or basic trigonometric ratios to determine missing side lengths required for area calculations.
Calculate the area of composite figures that include sectors and segments of circles.
Solve multi-step word problems involving the area of real-world compound figures.
Ever planned to paint a room with an alcove or design a garden with a curved path? You were already thinking about the area of compound figures! 🏡
This tutorial will teach you how to find the area of complex shapes by b...
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Key Concepts & Vocabulary
TermDefinitionExample
Compound FigureA two-dimensional shape made by combining two or more basic geometric shapes (e.g., rectangles, triangles, circles). It is also known as a composite figure.An L-shaped polygon can be seen as two rectangles joined together. A window shape could be a rectangle combined with a semicircle on top.
DecompositionThe strategic process of breaking a compound figure into simpler, non-overlapping shapes whose area formulas are known.Splitting an L-shaped figure into two distinct rectangles by drawing a single horizontal or vertical line.
Addition MethodA technique for finding the total area of a compound figure by calculating the area of each decomposed shape and then adding them together.For an ice-cream cone shape, you would find the area of the triangle and th...
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Core Formulas
Area Addition Principle
A_{total} = A_{1} + A_{2} + ... + A_{n}
Use this when the compound figure is formed by joining shapes together. Decompose the figure, find the area of each individual part (A_1, A_2, etc.), and sum them to get the total area.
Area Subtraction Principle
A_{shaded} = A_{larger} - A_{smaller}
Use this for figures with cutouts or holes. Identify the larger, encompassing shape and the smaller, removed shape. Calculate both areas and subtract the smaller from the larger.
Area of a Sector (Degrees)
A_{sector} = (\frac{\theta}{360}) \times \pi r^2
Use this to find the area of a pie-slice portion of a circle, where 'r' is the radius and 'θ' (theta) is the central angle of the sector in degrees.
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Challenging
Find the area of a circular segment created by a chord and a 90° arc in a circle with a radius of 8 cm. (Leave your answer in terms of π).
A.(16π - 32) cm²
B.(64π - 32) cm²
C.(16π - 64) cm²
D.16π cm²
Challenging
A composite figure is made of a rectangle and an attached triangle. The rectangle is 10m by 8m. The triangle is attached to the 8m side. The angle between the 8m side (base of the triangle) and the triangle's hypotenuse is 60°. Find the total area of the figure. (Use √3 ≈ 1.73).
A.135.68 m²
B.80 m²
C.107.72 m²
D.165.36 m²
Challenging
The total area of the L-shaped figure shown, which has only right angles, is 76 cm². The outer vertical length is 10 cm and the outer horizontal length is 9 cm. The inner vertical length is 4 cm. What is the length of the inner horizontal side, 'x'?
A.4 cm
B.5 cm
C.6 cm
D.7 cm
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Frequently asked questions
What grade level is "Area of compound figures"?
Area of compound figures is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Area of compound figures?
You'll be able to: Identify the key information (total, percent, part) in percent word problems with 80% accuracy; Solve percent of a number word problems using at least one strategy (e.g., converting percent to decimal, using proportions) and….
Is "Area of compound 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 of compound figures?
This lesson includes 31 practice questions across multiple difficulty levels, each with instant feedback and explanations.