Use 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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An illustration shows a trapezoid with the longer side on the left labeled as 12 inches. The opposite parallel side is 10 inches. Two perpendicular dotted lines extend from the vertices at either end of the 10 inch side to the longer side, and are labeled 8 inches. The two perpendicular lines are denoted by 4 right angle symbols.
An illustration shows a parallelogram with top side as 10 centimeters. A perpendicular dotted line from top left vertex to the bottom side is 8 centimeters. The perpendicular line makes one right angle symbol with top side and two right angle symbols with the bottom side.
An illustration shows a parallelogram with bottom side as 14 inches. A perpendicular dotted line from the bottom right vertex to the top side is 3 inches. The perpendicular line is denoted by two right angle symbols.
An illustration shows a parallelogram with top side as 7 centimeters. A perpendicular dotted line from the top left vertex to the bottom side is 12 centimeters. The perpendicular line makes one right angle symbol with the top side and two right angle symbols with the bottom side.
The area of the quadrilateral can be found by splitting it into two smaller shapes - a triangle and a trapezoid.
The triangle has a base of 6 centimeters and a height of 6 centimeters (since the dotted line is perpendicular to the top side), so its area is (1/2) * base * height = (1/2) * 6 * 6 = 18 cm^2.
The trapezoid has a top side of 6 centimeters, a bottom side of 10 centimeters, and a height of 6 centimeters. The formula for the area of a trapezoid is (1/2) * (sum of the parallel sides) * height. Therefore, the area of the trapezoid is (1/2) * (6 + 10) * 6 = 48 cm^2.
Adding the area of the triangle and the trapezoid together, the total area of the quadrilateral is 18 cm^2 + 48 cm^2 = 66 cm^2.
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Apologies for the confusion.
To find the area of the quadrilateral, we can use the formula for the area of a trapezoid:
Area = (1/2) * (sum of the parallel sides) * height
In this case, the sum of the parallel sides is 6 + 10 = 16 centimeters and the height is 6 centimeters.
Therefore, the area of the quadrilateral is:
Area = (1/2) * 16 * 6
Area = 48 cm^2
So, the area of the quadrilateral is 48 cm^2.