The area of a trapezium is 180cm2and its hight is 9cm .if one of the parallel side is longer than the other by 6cm ,find the two parallel sides
Answers
Area = 180cm²
Height = 9cm
Let the parallel sides be x and x + 6. The second parallel side is x + 6 because the question says that one of the parallel sides is longer than the other by 6cm.
Remember that to find the area of a trapezium, use the formula: Area = 1/2 × (sum of parallel sides) × height.
Substitute the given values into the formula.
180cm² = 1/2 × (x + x + 6) × 9cm
Move the 9cm over to the area and divide. (*The units are excluded for easier calculations.)
180 ÷ 9 = 1/2 × (x + x + 6)
20 = 1/2 × (x + x + 6)
Now, move the 1/2 over to 20 and divide. (Flip the fraction to multiply.)
20 ÷ 1/2 = x + x + 6
20 × 2/1 = x + x + 6
40/1 = x + x + 6
40 = x + x + 6
Add the x's.
40 = x + x + 6
40 = 2x + 6
Move the 6 over to 40 and subtract. (Flip the equation so it's easier.)
2x = 40 - 6
2x = 34
Lastly, divide 34 by 2.
x = 34 ÷ 2
x = 17
The first parallel side, x, is 17cm. The second parallel side, x + 6, is 23cm because 17 + 6 = 23.