To find the surface area of a trapezoidal prism, we first need to calculate the area of the two trapezoidal bases and then the area of the four rectangular sides.
The formula for the area of a trapezoid is 1/2 * (a + b) * h, where a and b are the bases of the trapezoid and h is the altitude.
For the top base, a = 7 yd, b = 4 yd, h = 3.5 yd:
Area of the top base = 1/2 * (7 + 4) * 3.5 = 17.5 sq yd
For the bottom base, a = 6 yd, b = 3 yd, h = 3.5 yd:
Area of the bottom base = 1/2 * (6 + 3) * 3.5 = 15.75 sq yd
Now we calculate the area of the four rectangular sides:
Side 1: 7 yd * 3.5 yd = 24.5 sq yd
Side 2: 4 yd * 3.5 yd = 14 sq yd
Side 3: 3 yd * 3.5 yd = 10.5 sq yd
Side 4: 6 yd * 3.5 yd = 21 sq yd
Now we sum up the areas:
Total surface area = 2(base area) + 4(side areas)
Total surface area = 2(17.5 + 15.75) + 4(24.5 + 14 + 10.5 + 21)
Total surface area = 65.5 + 2(2) + 4(70)
Total surface area = 65.5 + 4 + 280
Total surface area = 349.5 sq yd
Therefore, the surface area of the trapezoidal prism is approximately 349.5 square yards.
Find the surface area. Round your answer to the nearest tenth.
trapezoidal prism sides=7yd, 4yd, 3yd, 6yd, altitude=3.5 yd
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