se the image to answer the question.
An illustration shows a trapezoid with top side as 6 centimeters and bottom side as 10 centimeters. Two perpendicular dotted lines extend from the top vertices to the bottom side and are labeled 6 centimeters each. The two perpendicular lines are denoted by 4 right angle symbols.
What is the area of the quadrilateral?
(1 point)
cm2
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The area of the quadrilateral can be calculated by finding the area of the trapezoid and subtracting the area of the two right triangles formed by the perpendicular lines.
The area of a trapezoid is given by the formula A = 1/2 * (a + b) * h, where a and b are the lengths of the two parallel sides and h is the height.
In this case, a = 6 cm, b = 10 cm, and h = 6 cm (height of the trapezoid).
Plugging in the values, we get:
A = 1/2 * (6 + 10) * 6
A = 1/2 * 16 * 6
A = 8 * 6
A = 48 cm^2
The area of each right triangle can be calculated using the formula A = 1/2 * base * height. Since both triangles have a base of 6 cm and a height of 6 cm, each triangle has an area of:
A = 1/2 * 6 * 6
A = 18 cm^2
Since there are two right triangles, the total area of both triangles is:
Total area = 2 * 18 cm^2
Total area = 36 cm^2
Therefore, the area of the quadrilateral is:
48 cm^2 - 36 cm^2 = 12 cm^2
So, the area of the quadrilateral is 12 square centimeters.