Use the image to answer the question.
An illustration shows a trapezoid. The top side measures 48 millimeters and the bottom side measures 100 millimeters. A perpendicular dashed line measuring 50 millimeters is drawn from the top left vertex to the bottom side.
What is the area of the trapezoid?
To find the area of the trapezoid, we first need to find the height.
From the top left vertex, we drew a perpendicular dashed line to the bottom side, creating a right triangle. The hypotenuse of this right triangle is the height of the trapezoid.
Using the Pythagorean theorem, we can find the height:
Height^2 = 48^2 - 50^2
Height^2 = 2304 - 2500
Height^2 = 196
Height = √196
Height = 14 millimeters
Now that we have the height, we can find the area of the trapezoid using the formula:
Area = 1/2 (top side + bottom side) x height
Area = 1/2 (48 + 100) x 14
Area = 1/2 (148) x 14
Area = 74 x 14
Area = 1036 square millimeters
Therefore, the area of the trapezoid is 1036 square millimeters.