A parcel of land is 400 ft by 640 ft. the parcel is cut in half diagonally by a stream. How many acres are there in each half of the parcel?

A parcel of land is 400 ft by 640 ft. the parcel is cut in half diagonally by a stream. How many acres are there in each half of the parcel?

• A. 2.92 acres
• B. 2.50 acres
• C. 3.00 acres
• D. 1.50 acres

Answer: (A)

A diagonal cut across the rectangle divides it into two congruent right triangles, so each half has half the total area. The full parcel is 400 ft by 640 ft, giving 400 × 640 = 256,000 square feet. Half of that is 128,000 square feet per half. Since 1 acre equals 43,560 square feet, 128,000 ÷ 43,560 ≈ 2.94 acres. The closest option is 2.92 acres, so that is the best choice. (You can also verify with the triangle area: 0.5 × 400 × 640 = 128,000 sq ft, then convert to acres.)

A diagonal cut across the rectangle divides it into two congruent right triangles, so each half has half the total area. The full parcel is 400 ft by 640 ft, giving 400 × 640 = 256,000 square feet. Half of that is 128,000 square feet per half. Since 1 acre equals 43,560 square feet, 128,000 ÷ 43,560 ≈ 2.94 acres. The closest option is 2.92 acres, so that is the best choice. (You can also verify with the triangle area: 0.5 × 400 × 640 = 128,000 sq ft, then convert to acres.)