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
30 cm2
30 cm squared
54 cm2
54 cm squared
60 cm2
60 cm squared
24 cm2
24 cm squared
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To find the area of the quadrilateral, we can break it down into two shapes: a trapezoid and a right triangle.
The area of the trapezoid can be found using the formula: area = (1/2)(b1 + b2)h, where b1 and b2 are the lengths of the two parallel sides, and h is the height.
In this case, the lengths of the two parallel sides are 4 cm and 6 cm, and the height is 9 cm. Plugging these values into the formula:
area of trapezoid = (1/2)(4 + 6)(9)
area of trapezoid = (1/2)(10)(9)
area of trapezoid = 45 cm^2
The area of the right triangle can be found using the formula: area = (1/2)(base)(height). In this case, the base is 6 cm and the height is 5 cm:
area of triangle = (1/2)(6)(5)
area of triangle = 15 cm^2
Adding the areas of the trapezoid and the triangle together:
45 cm^2 + 15 cm^2 = 60 cm^2
Therefore, the area of the quadrilateral is 60 cm^2.
So, the answer is:
60 cm2
60 cm squared
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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To find the area of the quadrilateral in the image, we need to first calculate the area of the trapezoid.
The formula to calculate the area of a trapezoid is:
Area = (1/2) * (sum of parallel sides) * height
In this case, the parallel sides are the left side (10 inches) and the right side (16 inches). The height can be found using the Pythagorean Theorem for the right triangle at the bottom of the trapezoid.
The base of the right triangle is the difference between 16 inches and 6 inches (dotted line drawn from the top left vertex to the right side). So, the base of the right triangle is 10 inches.
Using the Pythagorean Theorem:
(10)^2 = (6)^2 + (height)^2
100 = 36 + height^2
height^2 = 64
height = 8 inches
Now we can calculate the area of the trapezoid:
Area = (1/2)(10 + 16) * 8
Area = (1/2)(26) * 8
Area = 13 * 8
Area = 104 square inches
Therefore, the area of the quadrilateral is 104 square inches.
So, the answer is:
104 in.2
104 in. squared
39 in.2
39 in. squared
78 in.2
78 in. squared
91 in.2
91 in. squared
96 in.2
To correctly calculate the area of the quadrilateral in the image, let's break it down into two shapes: a trapezoid and a right triangle.
First, let's calculate the area of the trapezoid:
The formula for the area of a trapezoid is:
Area = (1/2) * (sum of the parallel sides) * height
In this case, the sum of the parallel sides is 10 inches (left side) and 16 inches (right side), and the height is 6 inches (perpendicular line from top left vertex to the right side).
Plugging the values into the formula:
Area of trapezoid = (1/2) * (10 + 16) * 6
Area of trapezoid = (1/2) * 26 * 6
Area of trapezoid = 13 * 6
Area of trapezoid = 78 square inches
Next, let's calculate the area of the right triangle (bottom part of the trapezoid):
The base of the right triangle is 16 inches (right side of the trapezoid) and the height is 6 inches (perpendicular line from top left vertex to the right side).
Using the formula for the area of a triangle:
Area of triangle = (1/2) * base * height
Area of triangle = (1/2) * 16 * 6
Area of triangle = 48 square inches
Adding the two areas together:
78 (area of trapezoid) + 48 (area of triangle) = 126 square inches
Therefore, the correct area of the quadrilateral is 126 square inches.
So, the answer is:
126 in.2
126 in. squared