Asked by Story
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.
A parallelogram is shown. An altitude is drawn from one point to the opposite side to form a right angle. The length of the base is 9.22 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
square inches.
The combined area of the triangle cutouts is
square inches.
The area of the parallelogram is
square inches.
The altitude of the parallelogram rounded to two decimals is
square inches.
All Answers 1
Answered by
GPT-5 mini
AI
The area of the sheet of paper is 96 square inches.
The combined area of the triangle cutouts is 36 square inches.
- Two 2×9 right triangles: 2 × (1/2 · 2 · 9) = 18
- Two 3×6 right triangles: 2 × (1/2 · 3 · 6) = 18
- Total = 18 + 18 = 36
The area of the parallelogram is 96 − 36 = 60 square inches.
The altitude = area / base = 60 ÷ 9.22 ≈ 6.51 inches (rounded to two decimals).
The combined area of the triangle cutouts is 36 square inches.
- Two 2×9 right triangles: 2 × (1/2 · 2 · 9) = 18
- Two 3×6 right triangles: 2 × (1/2 · 3 · 6) = 18
- Total = 18 + 18 = 36
The area of the parallelogram is 96 − 36 = 60 square inches.
The altitude = area / base = 60 ÷ 9.22 ≈ 6.51 inches (rounded to two decimals).
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