A triangle is cut from a rectangular piece of fabric with dimensions of 55.2 feet by 45 feet. If the side lengths of the triangle are 17 feet, 20 feet, and 31 feet, what is the area of the leftover fabric? Round to the nearest tenth at the end of your calculations. Please help!
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Answer:
2328.2 feet²
Step-by-step explanation:
length of rectangular piece l = 55.2 feet
width of rectangular piece b = 45 feel
area of rectangular piece = l×b = 55.2×45 = 2484 feet²
area of triangle A = √s(s-a)(s-b)(s-c)
s = (a+b+c)÷2 where a,b,c are side length of tiangle
s = (17+20+31)÷2 = 68÷2 = 34
A = √34(34-17)(34-20)(34-30)
A = √34(17)(14)(3)
A = √24276 = 155.81 feet²
area of leftover fabric = (area of rectangular piece) - (area of triangular piece)
= 2484 - 155.81
= 2328.19 feet²
= 2328.2 feet²
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