Area and Formulas of Shapes

The video tutorial covers the concept of composite shapes and how to calculate their areas using addition and subtraction. It provides four examples: a rectangle with a circle, a rectangle with a triangle, a trapezoid with a circle cutout, and a pentagon with a rectangle cutout. Each example demonstrates the steps to determine the shapes, apply the correct formulas, and decide whether to add or subtract areas. The tutorial emphasizes the importance of understanding the geometry and using a calculator for precise results.

What is the first step in finding the area of composite shapes?

• Multiply the areas of the shapes

• Subtract the areas of the shapes

• Identify the shapes and their equations

• Calculate the total area directly

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CCSS.3.MD.C.7B

CCSS.4.MD.A.3

In the first example, what is the area of the rectangle?

• 45 inches squared

• 118.27 inches squared

• 28.27 inches squared

• 90 inches squared

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CCSS.7.G.B.4

How do you find the radius of the circle in the first example?

• Divide the diameter by 2

• Multiply the diameter by 2

• Subtract the diameter from the height

• Add the diameter to the height

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CCSS.6.G.A.1

In the second example, what is the formula for the area of a triangle?

• Base divided by height

• Base plus height

• 1/2 base times height

• Base times height

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CCSS.6.G.A.1

What is the total area of the shapes in the second example?

• 18 inches squared

• 36 inches squared

• 54 inches squared

• 72 inches squared

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CCSS.1.G.A.2

In the third example, what shape is being cut out from the trapezoid?

• Triangle

• Rectangle

• Square

• Circle

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CCSS.6.G.A.1

What is the area of the trapezoid in the third example?

• 202.23 meters squared

• 61.46 meters squared

• 78.54 meters squared

• 140 meters squared

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CCSS.6.G.A.1

In the final example, what is the formula for the area of a pentagon?

• Base times height

• 1/2 apothem times perimeter

• Apothem times perimeter

• 1/2 base times height

Tags

CCSS.6.G.A.1

How do you find the apothem of the pentagon in the final example?

• Multiplying the side length by 2

• Using the side length directly

• Dividing the side length by 2

• Using trigonometry

What is the final area of the shaded region in the last example?

• 337.05 feet squared

• 134.82 feet squared

• 202.23 feet squared

• 118.27 feet squared