Question

9 calculate the height ah of the trapezoid below.
my calculations

Explanation:

Step1: Identify the y-coordinate of A and H

Point \( A \) has coordinates \( (2, 4) \), and point \( H \) lies on the x - axis (since it's the foot of the perpendicular from \( A \) to the x - axis), so the y - coordinate of \( H \) is \( 0 \).

Step2: Calculate the height \( AH \)

The height of a trapezoid (the perpendicular distance between the two parallel sides) in this case, since \( AH \) is perpendicular to the x - axis, the length of \( AH \) is the difference between the y - coordinates of \( A \) and \( H \). Using the formula for the distance between two points with the same x - coordinate (\( x_1=x_2 = 2 \) for \( A(2,4) \) and \( H(2,0) \)): \( d=\vert y_1 - y_2\vert \).
Substitute \( y_1 = 4 \) and \( y_2=0 \) into the formula: \( AH=\vert4 - 0\vert=4 \).

Answer:

The height \( AH \) of the trapezoid is \( 4 \).