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skelet666 [1.2K]
3 years ago
15

hank orders popcorn while watching a movie. the popcorn was served in a trapezoidal bucket. the height of the bucket is 10x-9 cm

, and the length of its broad bases are 10x-2 cm and 16x+10cm. which of th following formulas can be used to find the area, A, of the broad side of the trapezoidal bucket
Mathematics
1 answer:
Gnoma [55]3 years ago
7 0

Area of the trapezoidal bucket, A is 130x² - 77x - 36 cm²

Step-by-step explanation:

  • Step 1: Area of a trapezoid = 1/2 (Sum of parallel sides) × Height

Sum of parallel sides = (10x - 2) + (16x + 10)

                                   = 26x + 8 = 2(13x + 4)

Height = 10x - 9

⇒ Area of the bucket = 1/2 × 2(13x + 4) (10x - 9)

                                    = (13x + 4)(10x - 9) cm²

                                    = 130x² - 117x + 40x - 36

                                A = 130x² - 77x - 36

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Answer:

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Step-by-step explanation:

Given that the regular polygon is a square, there are multiple ways you can jump directly to the answer. Perhaps the simplest is to use the formula for the area of a rhombus:

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where d1 and d2 are the lengths of the diagonals. Here, we see that half the diagonal is 5 cm, so the area is ...

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The formula is somewhat different if you start with the length of the apothem. One way to find the area is using the above formula and the relation between the radius and apothem:

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Another formula uses the apothem directly:

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