A trapezoid with an area of 48m2 has a height of 6m. One of its bases is 12m. Write and solve an equation to find the length of its other base.
Also explain the work so I can understand when I do the test. Thanks
area of trap
= (1/2)(sum of parallel sides)(distance between them)
(1/2(a + 12)(6) , where a is the other parallel side.
(1/2(a + 12)(6) = 48
3(a+12) = 48
3a + 36 = 48
3a = 12
a = 4
area=height(12+base2)/2
solve for base2
To find the length of the other base of the trapezoid, we can use the formula for the area of a trapezoid which is given by:
Area = (1/2) * (base1 + base2) * height
In this case, we are given that the area is 48m^2, the height is 6m, and one of the bases is 12m. Let's assume the length of the other base is 'x'.
So the equation becomes:
48 = (1/2) * (12 + x) * 6
To solve this equation, we can start by simplifying the expression on the right side:
48 = (1/2) * (12 + x) * 6
48 = (6/2) * (12 + x)
48 = 3 * (12 + x)
Next, we can divide both sides of the equation by 3:
48/3 = 3 * (12 + x) / 3
16 = 12 + x
Now, we can isolate 'x' by subtracting 12 from both sides:
16 - 12 = x
4 = x
Therefore, the length of the other base of the trapezoid is 4m.
Let me know if you need any further assistance!
To find the length of the other base of the trapezoid, we can use the formula for the area of a trapezoid:
Area = (1/2) * (Sum of the bases) * Height
First, let's label the length of the other base as x.
Given conditions:
Area = 48m²
Height = 6m
One base = 12m
Other base = x
Using the formula: Area = (1/2) * (Sum of the bases) * Height
48 = (1/2) * (12 + x) * 6
Now, let's solve for x.
First, we can simplify the equation by multiplying both sides by 2 to get rid of the fraction:
2 * 48 = 6 * (12 + x)
96 = 72 + 6x
Next, subtract 72 from both sides to isolate the variable (6x):
96 - 72 = 6x
24 = 6x
Divide both sides by 6 to solve for x:
24/6 = 6x/6
4 = x
Therefore, the length of the other base of the trapezoid is 4 meters.
To summarize, the equation we used to solve for the length of the other base of the trapezoid was:
48 = (1/2) * (12 + x) * 6
We simplified and solved the equation to find that x = 4.