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
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.
To find the area of a trapezoid, you can use the formula:
Area = 1/2 * (sum of the bases) * height
In this case, the top base of the trapezoid is 7 meters, the bottom base is 11 meters, and the height is not given. Therefore, we cannot determine the area of the trapezoid without knowing the height.