Use the image to answer the question.
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.
What is the area of the quadrilateral?
(1 point)
Responses
96 in.2
96 in. squared
91 in.2
91 in. squared
78 in.2
78 in. squared
39 in.2
39 in. squared
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To find the area of the quadrilateral, we need to break it down into two triangles and a rectangle.
First, we calculate the area of the triangle on the left side:
Area of left triangle = (1/2) * base * height
Area = (1/2) * 10 * 6 = 30 in^2
Next, we calculate the area of the triangle on the right side:
Area of right triangle = (1/2) * base * height
Area = (1/2) * 16 * 6 = 48 in^2
Finally, we calculate the area of the rectangle in the middle:
Area of rectangle = base * height
Area = 7 * 6 = 42 in^2
Now, we add up all the areas:
30 + 48 + 42 = 120 in^2
Therefore, the area of the quadrilateral is 120 in^2.
thats wrong
To find the area of the quadrilateral, we first need to find the height of the trapezoid. This can be done by using the Pythagorean theorem on the right triangle formed by the height, 6 inches and the difference between the two bases (16 - 10 = 6) inches.
Using the Pythagorean theorem:
height = √(7^2 - 6^2)
height = √(49 - 36)
height = √13
Now, we calculate the area of the trapezoid:
Area = (1/2) * (10 + 16) * √13
Area = 13 * √13
Area ≈ 39 in^2
Therefore, the area of the quadrilateral is approximately 39 in^2. The closest answer choice is:
39 in.2