Rose's garden is in the shape of a trapezoid. If the height of the trapezoid is 16m, one base is 20m, and the area is 224 m squared, find the length of the other base.
The height dimension h is measure perpendicular to the to parallel "base" sides, a and b.
The area is h*(a+b)/2 = 224
You know a and h, so solve for b.
Find the area of a trapezoid with bases of 4 cm and 11 cm and a height of 7 cm if A = 1/2(b1 + b2)h.
16
Given:
Height (h) = 16m
One base (a) = 20m
Area (A) = 224 m²
Formula:
Area of a trapezoid = (h * (a + b))/2
Substituting the given values:
224 = (16 * (20 + b))/2
Simplifying the equation:
224 = (16 * 20 + 16 * b)/2
224 = (320 + 16b)/2
2 * 224 = 320 + 16b
448 = 320 + 16b
16b = 448 - 320
16b = 128
Solving for b:
b = 128/16
b = 8
Therefore, the length of the other base (b) is 8m.
To find the length of the other base of the trapezoid, we can use the formula for the area of a trapezoid:
Area = (h * (a + b)) / 2
Where:
- Area is the given area of the trapezoid (224 m^2)
- h is the height of the trapezoid (16 m)
- a is one of the bases (20 m)
- b is the length of the other base (unknown)
We can rearrange the formula to solve for b:
2 * Area = h * (a + b)
2 * 224 = 16 * (20 + b)
448 = 16 * (20 + b)
448 = 320 + 16b
128 = 16b
To isolate b, divide both sides of the equation by 16:
8 = b
Therefore, the length of the other base of the trapezoid is 8 m.