Rose’s garden is in the shape of a trapezoid. If the height of the trapezoid is 16 m, one base is 20 m, and the area is 224 m2, find the length of the other base.
How do I set up this problem so I can solve it?
Thank you!
so, what is the function for the area of a trapezoid?
I'm still confused, what do you mean?
area=1/2*(base+ top)*height
solve for top.
To solve this problem, we need to equate the given information about the trapezoid to the formula for the area of a trapezoid.
The formula for the area of a trapezoid is: A = (1/2) * (b1 + b2) * h
Where:
A is the area of the trapezoid,
b1 is the length of one base of the trapezoid,
b2 is the length of the other base of the trapezoid, and
h is the height of the trapezoid.
Using the given information:
- The height of the trapezoid is given as 16 m, so h = 16.
- One base of the trapezoid is given as 20 m, so b1 = 20.
- The area of the trapezoid is given as 224 m^2, so A = 224.
Now, we can substitute these values into the formula and solve for b2:
224 = (1/2) * (20 + b2) * 16
To solve for b2, we need to isolate it on one side of the equation. Let's continue solving the equation:
224 = (1/2) * (20 + b2) * 16
224 = (10 + (b2/2)) * 16
224/16 = 10 + (b2/2)
14 = 10 + (b2/2)
14 - 10 = b2/2
4 = b2/2
To solve for b2, we multiply both sides of the equation by 2:
2 * 4 = 2 * (b2/2)
8 = b2
Therefore, the length of the other base (b2) is 8 m.