Adding and Subtracting Rational Expressions

The video tutorial explains how to calculate the area of composite figures by breaking them into basic shapes like triangles, parallelograms, trapezoids, rectangles, and circles. It provides step-by-step examples, including a parallelogram with semicircles, a cone with a semicircle and triangle, a figure with a square, triangle, and trapezoid, and a rectangle with a trapezoid. The tutorial emphasizes simplifying complex figures and using known formulas to find areas, rounding results as necessary.

What is a composite figure?

• A figure that cannot be divided

• A figure that can be divided into simpler known shapes

• A figure made up exclusively of triangles

• A figure made up of only circles

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CCSS.1.G.A.2

How do you find the area of a composite figure?

• By multiplying the dimensions of the composite figure

• By measuring the figure with a ruler

• By using calculus

• By adding the areas of the simpler component shapes

What shapes make up the composite figure discussed first in the video?

• A parallelogram and two semicircles

• Two triangles and a rectangle

• A circle and a square

• Four parallelograms

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CCSS.1.G.A.2

What is the area of a circle if the diameter is 12 units?

• 113.1 square units

• 226.2 square units

• 452.4 square units

• 56.5 square units

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CCSS.7.G.B.4

How is the height of the triangle in the cone figure determined?

• Using the area formula directly

• By direct measurement

• Using the Pythagorean theorem

• Estimation

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CCSS.6.G.A.1

What strategy is suggested for handling complex composite figures?

• Using advanced mathematical formulas

• Consulting a mathematician

• Ignoring the complexity

• Dividing them into as few regions as possible

What is the area of the square in the complex figure discussed?

• 400 square units

• 100.53 square units

• 314.16 square units

• 207.36 square units

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CCSS.3.MD.C.7B

CCSS.4.MD.A.3

What is the total area of the composite figure involving a rectangle, triangle, and semicircle?

• 325.23 square feet

• 200 square feet

• 500 square feet

• 150 square feet

How is the side of the rectangle determined in the final example?

• By multiplying the radius by two

• By adding the radius to the total length

• By subtracting the radius of the semicircle from the total length

• By dividing the total length by two

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CCSS.3.MD.D.8

What is the correct approach to calculate the area of a kite-shaped figure?

• Using the product of its diagonals

• Summing the lengths of all sides

• Calculating the circumference

• Using the radius of a circumscribed circle

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CCSS.6.G.A.1