Question

a parallelogram is cut out of a 12-inch by 8-inch sheet of paper. there are four right triangle remnants. two have the dimensions 2 inches by 9 inches, and the other two have the dimensions 3 inches by 6 inches. the resulting parallelogram has a base of approximately 9.22 inches. complete the following steps to calculate the altitude of the parallelogram using area methods. the area of the sheet of paper is \boxed{} square inches. the combined area of the triangle cutouts is \boxed{} square inches. the area of the parallelogram is \boxed{} square inches. the altitude of the parallelogram rounded to two decimals is \boxed{} square inches.

Explanation:

Step1: Calculate sheet area

Area = length × width = $12 \times 8 = 96$

Step2: Calculate area of small triangles

Area of 2 triangles: $2 \times \frac{1}{2} \times 2 \times 9 = 18$

Step3: Calculate area of large triangles

Area of 2 triangles: $2 \times \frac{1}{2} \times 3 \times 6 = 18$

Step4: Total cutout area

Sum of triangle areas: $18 + 18 = 36$

Step5: Calculate parallelogram area

Sheet area - cutout area: $96 - 36 = 60$

Step6: Calculate parallelogram altitude

Altitude = $\frac{\text{Area}}{\text{Base}} = \frac{60}{9.22} \approx 6.51$

Answer:

The area of the sheet of paper is 96 square inches.
The combined area of the triangle cutouts is 36 square inches.
The area of the parallelogram is 60 square inches.
The altitude of the parallelogram rounded to two decimals is 6.51 inches.