Mathematics
Grade 10
15 min
Area and perimeter mixed review
Area and perimeter mixed review
What you'll learn
- Identify the fraction of a whole that is shaded in a given picture with at least 80% accuracy.
- Convert a shaded fraction (with denominators of 2, 4, 5, 10, 20, 25, 50, and 100) into a percentage with 100% accuracy.
- Explain how a fraction, a decimal, and a percentage can all represent the same part of a whole using examples with at least two different representations.
- Solve word problems involving identifying the percentage represented by a shaded portion of a shape with at least 75% accuracy.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Calculate the area and perimeter of complex composite figures by decomposing them into simpler shapes.
Apply the Pythagorean theorem and trigonometric ratios (SOH CAH TOA) to determine unknown side lengths required for area and perimeter calculations.
Determine the perimeter and area of polygons defined by vertices on a coordinate plane using the distance formula.
Calculate the arc length and area of sectors of circles and incorporate them into composite figure problems.
Calculate the area of regular polygons using the apothem and perimeter formula.
Analyze word problems to distinguish between scenarios requiring area, perimeter, or both, and develop a multi-step solution strategy.
Imagine you're designing a custom skate park or landscaping a backyar...
2
Key Concepts & Vocabulary
TermDefinitionExample
Composite FigureA two-dimensional figure made up of two or more basic geometric shapes such as triangles, rectangles, and circles.An 'L-shaped' room can be seen as two rectangles combined. Its area is the sum of the areas of the two rectangles.
Apothem (of a Regular Polygon)A line segment from the center of a regular polygon to the midpoint of a side, to which it is perpendicular.In a regular hexagon, the apothem is the height of one of the six equilateral triangles that form the hexagon, if you connect the vertices to the center.
Sector of a CircleThe portion of a circle enclosed by two radii and the arc that connects them.A slice of pizza is a perfect example of a sector of a circle.
Arc LengthThe distance along the curved line making up an arc, which is...
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Core Formulas
Area of a Regular Polygon
A = \frac{1}{2}aP
Used to find the area of a regular polygon. 'A' is the area, 'a' is the length of the apothem, and 'P' is the perimeter of the polygon.
Arc Length and Sector Area
Arc Length (L) = \frac{\theta}{360°} \times 2\pi r \quad | \quad \text{Sector Area (A)} = \frac{\theta}{360°} \times \pi r^2
Used to find the length of a part of a circle's circumference or the area of a 'slice' of a circle. 'θ' is the central angle in degrees and 'r' is the radius.
Distance Formula
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
Used in coordinate geometry to find the distance between two points (x₁, y₁) and (x₂, y₂). This is essential for finding the perimeter of polygons on a coordinate...
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Challenging
A regular hexagon is centered at the origin, and one of its vertices is at the point V(4, 4√3). What is the exact area of the hexagon?
A.128√3
B.192√3
C.96√3
D.64√3
Challenging
A chord of a larger circle is tangent to a smaller, concentric circle. If the length of the chord is 12 cm, what is the exact area of the annulus (the region between the two circles)?
A.36π cm²
B.144π cm²
C.12π cm²
D.72π cm²
Challenging
A standard running track has a total perimeter of 400 meters. The track consists of two 100-meter straight sections and two semicircular ends. What is the distance between the two straight sections?
A.100/π m
B.200π m
C.100π m
D.200/π m
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Frequently asked questions
What grade level is "Area and perimeter mixed review"?
Area and perimeter mixed review is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Area and perimeter mixed review?
You'll be able to: Identify the fraction of a whole that is shaded in a given picture with at least 80% accuracy; Convert a shaded fraction (with denominators of 2, 4, 5, 10, 20, 25, 50, and 100) into a percentage with 100% accuracy; Explain how a….
Is "Area and perimeter mixed review" 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 mixed review?
This lesson includes 47 practice questions across multiple difficulty levels, each with instant feedback and explanations.