a trapezoid has an area of 4 square units and a height of 1 unit what are the possible lengths and bases
recall that area of trapezoid is
A = (b1 + b2)*(h/2)
where
b1 and b2 are the bases of trapezoid
h is the height
substituting,
4 = (b1 + b2) * (1/2)
8 = b1 + b2
now we list two number whose sum is 8:
1 and 7
2 and 6
3 and 5
4 and 4
these are the possible lengths of bases.
hope this helps~ :)
Thank You!
To find the possible lengths and bases of a trapezoid with a given area and height, we can use the formula for the area of a trapezoid:
Area = (1/2) * (b1 + b2) * h,
where b1 and b2 are the lengths of the bases, and h is the height.
In this case, we have the area (A) as 4 square units and the height (h) as 1 unit.
Plugging these values into the formula, we get:
4 = (1/2) * (b1 + b2) * 1.
Simplifying this equation, we have:
8 = b1 + b2.
Now, the lengths of the bases (b1 and b2) can be any pair of numbers that add up to 8.
Some possible combinations of lengths for the bases could be:
- b1 = 1, b2 = 7
- b1 = 2, b2 = 6
- b1 = 3, b2 = 5
- b1 = 4, b2 = 4
These are just a few examples, but there are many more possible combinations of lengths for the bases as long as they add up to 8.