Exploring Adding and Subtracting Rational Expressions

The video tutorial covers the calculation of areas for composite figures, which are shapes that can be divided into simpler geometric figures like rectangles, trapezoids, and circles. It provides step-by-step examples, including a rectangle with a trapezoid, a parallelogram with semicircles, and a semicircle with an isosceles triangle. The tutorial also explains how to find the area of shaded regions by subtracting the area of non-shaded parts. Key concepts include using formulas for basic shapes, applying the Pythagorean theorem, and understanding the subtraction method for shaded areas.

What is the first step in calculating the area of a composite figure?

• Find the longest side of the figure

• Add the areas of all shapes together

• Calculate the perimeter of the figure

• Divide the figure into simpler shapes

What is the area of the rectangle in the first composite figure example?

• 276 cm²

• 114 cm²

• 153 cm²

• 390 cm²

How do you calculate the area of a trapezoid?

• π × Radius²

• 1/2 × (Base1 + Base2) × Height

• Base × Height

• Length × Width

What is the combined area of the parallelogram and the two semicircles?

• 173.10 in²

• 220.53 m²

• 117.83 m²

• 134.13 ft²

How is the area of a semicircle calculated in the context of composite figures?

• π × Radius

• π × Radius² ÷ 2

• Base × Height ÷ 2

• Length × Width

What theorem is used to find the height of the isosceles triangle in the composite figure?

• Euclidean theorem

• Pythagorean theorem

• Thales' theorem

• Binomial theorem

What is the area of the shaded region in the example involving a square and a circle?

• 134.13 ft²

• 173.10 in²

• 117.83 m²

• 220.53 m²

How do you find the area of a shaded region?

• Divide the total area by the area of the non-shaded part

• Add the area of the shaded and non-shaded parts

• Multiply the areas of the shaded and non-shaded parts

• Subtract the area of the non-shaded part from the total area

What is the radius of the circle in the last shaded region example?

• 12.5 m

• 9 m

• 11.7 m

• 23.4 m

What is the final area of the composite figure involving a right triangle and a circle?

• 117.83 m²

• 97.2 m²

• 134.13 ft²

• 215.03 m²