Work out the area of this trapezium
6cm
10cm
8cm
17cm

  (81√15)/4 ≈ 78.43 cm²

Step-by-step explanation:

It can help to draw a diagram.

The base angle at the side of length 6 can be found using the Law of Cosines. Its opposite side is of length 8, and the two adjacent sides are of length 6 and 7. So, we have ...

  8² = 6² +7² -2·6·7·cos(α)

  cos(α) = (36+49-64)/(84) = 1/4

  α = arccos(1/4) ≈ 75.522°

Then the height of the trapezium is ...

  6·sin(75.522°) ≈ 5.80948 . . . . cm

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The area of the trapezium is given by the formula ...

  A = 1/2(b1 +b2)h

  A = (1/2)(17 +10)(5.80948) . . . . cm²

  A ≈ 78.43 cm²

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Of course, sin(arccos(1/4)) = (√15)/4, so the exact formulation of the area is ...

  A = (81√15)/4 cm²

5x+40

5(x + 8)

7x - 49

7(x - 7)

18x + 9

9(2x + 1)

15x - 10

5(3x - 2)

step-by-step explanation:

for number one all you have to do is factor 5 out of 5x + 40

for number 2 factor 7 out of 7x - 49

for number three factor 9 out of 18x + 9

for number four factor 5 out of 15x - 10

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step-by-step explanatio89