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
39 in.2
39 in. squared
78 in.2
78 in. squared
91 in.2
91 in. squared
96 in.2
96 in. squared
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91 in.2
91 in. squared
To find the area of the trapezoid, you can split it into two triangles. The area of a triangle is 1/2 * base * height.
The area of the top triangle = 1/2 * 7 * 6 = 21 in²
The area of the bottom triangle = 1/2 * 10 * 6 = 30 in²
Adding the areas of the two triangles together, we get 21 + 30 = 51 in². But since the trapezoid is made up of two triangles, we have to double the area, so 51 * 2 = 102 in².
Therefore, the area of the quadrilateral is 102 in².
wrong its one of these
39 in.2
39 in. squared
78 in.2
78 in. squared
91 in.2
91 in. squared
96 in.2
To find the area of the trapezoid, we need to calculate the area of the two triangles as described in the previous response:
The area of the top triangle = 1/2 * 7 * 6 = 21 in²
The area of the bottom triangle = 1/2 * 10 * 6 = 30 in²
Adding the areas of the two triangles together, we get 21 + 30 = 51 in². Since there are two equal triangles, we multiply by 2 to get the total area of the quadrilateral:
51 * 2 = 102 in²
As a result, the correct answer should be:
78 in.2 or 78 in. squared
Use the image to answer the question.
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.
What is the area of the quadrilateral?
(1 point)
Responses
460 cm2
460 cm squared
240 cm2
240 cm squared
480 cm2
480 cm squared
220 cm2
220 cm squared
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Use the image to answer the question.
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.
What is the area of the quadrilateral?
(1 point)
Responses
112 in.2
112 in. squared
102 in.2
102 in. squared
80 in.2
80 in. squared
140 in.2
140 in. squared
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To find the area of the parallelogram, we use the formula:
Area = base * height
The base of the parallelogram, which is the slanted side, is 10 inches. The height can be calculated using the Pythagorean theorem by considering the right triangle formed by the 8-inch perpendicular line and the height from the top right vertex to the left side.
Using Pythagorean theorem:
h^2 + 8^2 = 14^2
h^2 + 64 = 196
h^2 = 132
h = √132
h ≈ 11.49 inches
Now, we can calculate the area:
Area = 10 * 11.49
Area ≈ 114.9 in²
Therefore, the area of the quadrilateral is approximately 114.9 in².
Among the given options, the closest answer is:
112 in.2 or 112 in. squared.
Use the image to answer the question.
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.
What is the area of the quadrilateral?
(1 point)
Responses
125 cm2
125 cm squared
100 cm2
100 cm squared
75 cm2
75 cm squared
80 cm2
80 cm squared
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To find the area of the trapezoid, we first need to find the height of the trapezoid which can be calculated using the Pythagorean theorem.
The height can be obtained as follows:
h^2 + 10^2 = 24^2
h^2 + 100 = 576
h^2 = 476
h = √476
h ≈ 21.83 cm
Now that we have the height, we can calculate the area of the trapezoid using the formula:
Area = 1/2 * (sum of parallel sides) * height
Area = 1/2 * (24 + 20) * 21.83
Area = 1/2 * 44 * 21.83
Area = 22 * 21.83
Area = 480.26 cm²
Therefore, the area of the quadrilateral is approximately 480 cm².
So the correct response among the given options is:
480 cm²
To find the area of the parallelogram, we can calculate the area using the formula:
Area = base * height
In this case, the base of the parallelogram is the slanting side which is 5 centimeters. The height can be calculated using the Pythagorean theorem:
h^2 + 4^2 = 25^2
h^2 + 16 = 625
h^2 = 609
h = √609
h ≈ 24.65 cm
Now, we can calculate the area:
Area = 5 * 24.65
Area ≈ 123.25 cm²
Therefore, the area of the quadrilateral is approximately 123.25 cm².
Among the provided options, the closest answer is:
125 cm2 or 125 cm squared.