16.1 Independent Practice

Rearrange the parts of the parallelogram to form a rectangle. Find the area of the parallelogram and the area of the rectangle. What is the relationship between the areas?

• Area of parallelogram = base × height = 14 cm × 6 cm = 84 cm². The area of the rectangle formed is also 84 cm². The areas are equal.

• Area of parallelogram = base × height = 14 cm × 6 cm = 84 cm², but the rearranged rectangle mistakenly uses half the height making its area 42 cm², so they are not equal.

• Area of parallelogram = 14 cm × 6 cm = 84 cm², whereas the rectangle is assumed to have dimensions 14 cm by 8 cm giving an area of 112 cm², hence they differ.

• Area of parallelogram is computed by adding the base and height (14 cm + 6 cm = 20 cm²) while the rectangle's area is wrongly calculated as 20 cm²; these methods are incorrect.

What is the area of a parallelogram that has a base of 12 3/4 in. and a height of 2 1/2 in.?

• Area = base × height = 12.75 × 2.5 = 31.875 in².

• Area = base + height = 12.75 + 2.5 = 15.25 in².

• Area = 2(base + height) = 2(12.75 + 2.5) = 30.5 in².

• Area = (base × height) / 2 = (12.75 × 2.5) / 2 = 15.9375 in².

Draw a copy of the trapezoid to form a parallelogram. Find the area of the trapezoid and the area of the parallelogram. What is the relationship between the areas?

• Area of trapezoid = 1/2 × (base1 + base2) × height = 1/2 × (42 + 36) × 24 = 1/2 × 78 × 24 = 39 × 24 = 936 in². The area of the parallelogram formed by doubling the trapezoid is 1872 in². The area of the trapezoid is half the area of the parallelogram.

• Area of the trapezoid is equal to the area of the parallelogram.

• Area of the trapezoid is twice the area of the parallelogram.

• Area of the trapezoid cannot be determined without more information.

The bases of a trapezoid are 11 meters and 14 meters. Its height is 10 meters. What is the area of the trapezoid?

• 125 m².

• 150 m².

• 130 m².

• 135 m².

The seat of a bench is in the shape of a trapezoid with bases of 6 feet and 5 feet and a height of 1.5 feet. What is the area of the seat?

• 8.25 ft².

• 7.5 ft².

• 9.5 ft².

• 8.75 ft².

A kite in the shape of a rhombus has diagonals that are 25 inches long and 15 inches long. What is the area of the kite?

• 187.5 in².

• 150 in².

• 300 in².

• 225 in².

A window in the shape of a parallelogram has a base of 36 inches and a height of 45 inches. What is the area of the window?

• Area = base × height = 36 × 45 = 1620 in².

• Area = base + height = 36 + 45 = 81 in².

• Area = (base × height)/2 = (36 × 45)/2 = 810 in².

• Area = base² + height² = 36² + 45² = 1296 + 2025 = 3321 in².

Communicate Mathematical Ideas: Find the area of the figure. Explain how you found your answer.

• Area of rectangle = 18 × 12 = 216 ft². Area of triangle = 1/2 × 10 × 6 = 30 ft². Total area = 216 + 30 = 246 ft². I found the area by adding the area of the rectangle and the triangle.

• Area of rectangle = 18 × 10 = 180 ft². Area of triangle = 1/2 × 12 × 6 = 36 ft². Total area = 180 + 36 = 216 ft². I mistakenly used different dimensions for the rectangle and triangle.

• Area of rectangle = 20 × 12 = 240 ft². Area of triangle = 1/2 × 10 × 6 = 30 ft². Total area = 240 + 30 = 270 ft². I calculated the area with an incorrect length for the rectangle.

• Area of rectangle = 18 × 12 = 216 ft². Area of triangle = 1/2 × 8 × 6 = 24 ft². Total area = 216 + 24 = 240 ft². I computed the triangle's area using a wrong base measurement.