The formula for the area of a trapezoid is:
A = (b1 + b2)h/2
Where b1 and b2 are the lengths of the top and bottom of the trapezoid, and h is the height.
In this case, b1 = 7m, b2 = 11m, and h is unknown. However, we can use the fact that the middle of the trapezoid is 5m to find the height.
The height of a trapezoid is the perpendicular distance between the top and bottom bases. In this case, we can draw a line from the middle of the trapezoid perpendicular to the top and bottom bases, creating two right triangles.
Using the Pythagorean theorem, we can find the height:
h^2 = (11m - 7m/2)^2 + 5m^2
h^2 = (9m)^2 + 5m^2
h^2 = 81m^2 + 25m^2
h^2 = 106m^2
h = sqrt(106)m
Now that we know the height, we can plug in the values to the formula for the area:
A = (7m + 11m) * sqrt(106)m/2
A = 18m * sqrt(106)m/2
A = 9m * sqrt(106)m
Therefore, the area of the trapezoid is 9m * sqrt(106)m, simplified.
Find the area of the the given geometric figure the top of the trapezoid 7m the middle 5m the bottom 11m the area of the trapezoid is? Simplify your answer
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