To find the area of the quadrilateral, we need to first find the area of the smaller right triangle at the bottom of the trapezoid.
Using the Pythagorean Theorem, we can calculate the height of the triangle:
a^2 + b^2 = c^2
6^2 + x^2 = 5^2
36 + x^2 = 25
x^2 = 25 - 36
x^2 = -11 (discard because it cannot be negative)
Therefore, the height of the triangle is 0.
Since the height is 0, the area of the triangle is also 0. Therefore, the area of the quadrilateral remains the same as the area of the trapezoid.
Now, to calculate the area of the trapezoid:
Area = (1/2) * (sum of parallel sides) * (height)
Area = (1/2) * (9 + 6) * 4
Area = (1/2) * 15 * 4
Area = 30 cm²
Therefore, the area of the quadrilateral is 30 cm².
Use the image to answer the question.
An illustration shows a trapezoid with top side as 4 centimeters, and the left as the longest side of 9 centimeters. The opposite parallel side on the right is 6 centimeters. A diagonal bottom side is 5 centimeters. The top side is perpendicular to the left and right sides as denoted by right two angle symbols. A perpendicular dotted line from the bottom right vertex to the left side is drawn. The dotted line makes one right angle symbol with right side and two right angle symbols with the left side. It forms a right triangle at the bottom of the trapezoid, with the 5 centimeter side as the hypotenuse.
Find the area of the quadrilateral.
(1 point)
Responses
60 cm2
60 cm squared
24 cm2
24 cm squared
54 cm2
54 cm squared
30 cm2
30 cm squared
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An illustration shows a trapezoid with parallel sides on the left and right. The left side is 10 inches and right side is 16 inches. The top slanting side is labeled 7 inches. Two perpendicular dotted lines of 6 inches each are drawn from the top and bottom left vertices to the right side.
An illustration shows a trapezoid with parallel sides on the top and bottom. The top side is 24 centimeters and bottom side is 20 centimeters. Two perpendicular dotted lines of 10 centimeters are drawn from the bottom vertices to the top side. The two perpendicular lines are denoted by 4 right angle symbols.
An illustration shows a parallelogram. The top side, slanted downward, is 10 inches. The left side is 14 inches. A dotted perpendicular line is drawn from top right vertex to the left side and labeled as 8 inches. It is denoted by one right angle symbol on the right and two right angle symbols on the left.
An illustration shows a parallelogram. The top side, slanting downward, is 5 centimeters, and the right side is 25 centimeters. A dotted perpendicular line is drawn from top right vertex to the left side and is labeled as 4 centimeters. It is denoted by two right angle symbols formed with the two sides.
1 answer