The area of trapezoid is h( b1+b2)/5,where h is the altitude, and b1 and b2 are the lenghts of the parallel bases. If trapezoid has an altitude of 5 inches, an area of 55 square inches , and one base 12 inches long, what is the length, in inches, of its other base?
A = h( b1+b2)/2
not over 5 I think
No need to think. Just write the equation down and plug in the numbers:
55 = 5 (12+b2)/2
22 = 12+b2
b2 = 10
Well, let's use some humor to solve this problem.
Since the formula for the area of a trapezoid is "h(b1 + b2)/5", it's like calculating the punchlines of a joke - you need all the right elements to make it work.
We know the altitude is 5 inches, and the area is 55 square inches. Now we're told that one of the bases is 12 inches.
Let's plug in the values and solve for the missing base, which we'll call "b2".
Using the equation 55 = (5 * (12 + b2))/5, we can simplify it to 55 = 12 + b2.
Next, let's subtract 12 from both sides of the equation.
55 - 12 = b2.
So, the length of the other base, b2, would be 43 inches.
And that's no joke! You've got yourself a trapezoid with a base of 12 inches and another base of 43 inches.
We are given:
Altitude (h) = 5 inches
Area = 55 square inches
Length of one base (b1) = 12 inches
We need to find the length of the other base (b2).
Using the formula for the area of a trapezoid: A = (h * (b1 + b2)) / 2
Substituting the given values: 55 = (5 * (12 + b2)) / 2
Multiplying both sides of the equation by 2: 110 = 5 * (12 + b2)
Dividing both sides of the equation by 5: 22 = 12 + b2
Subtracting 12 from both sides of the equation: b2 = 22 - 12
Therefore, the length of the other base (b2) is 10 inches.
To find the length of the other base of the trapezoid, we can rearrange the formula for the area of a trapezoid.
The formula you provided is: Area = h(b1 + b2) / 2
Given that the altitude (h) is 5 inches, and the area is 55 square inches, we can substitute these values into the formula:
55 = 5(b1 + b2) / 2
Multiplying both sides by 2:
110 = 5(b1 + b2)
Now we can substitute the length of one base (b1 = 12 inches) into the equation:
110 = 5(12 + b2)
Next, simplify the equation:
110 = 60 + 5b2
Subtract 60 from both sides:
110 - 60 = 5b2
50 = 5b2
Divide both sides by 5:
10 = b2
Therefore, the length of the other base (b2) is 10 inches.