What is the area of the trapezoid? The diagram is not drawn to scale. The lower interior angles are marked congruent. Two dashed segments are graphed from the vertices of the top side to the lower side and are each marked perpendicular to the lower side. The top side equals 8 centimeters. The left dashed segment equals 6 centimeters. The right part of the lower side between the right dashed segment and the vertex is 4 centimeters. (1 point) Responses 48 cm2 48 cm 2 64 cm2 64 cm 2 72 cm2 72 cm 2 104 cm2
To find the area of the trapezoid, we can divide it into two triangles and a rectangle.
First, we find the height of the trapezoid by finding the difference in height between the two dashed segments. The height is 6 - 4 = 2 centimeters.
Next, we find the area of each triangle. The area of a triangle is given by the formula: area = 0.5 * base * height.
For the triangle on the left side, the base is 6 centimeters and the height is 2 centimeters.
So, the area of the left triangle is: 0.5 * 6 * 2 = 6 cm^2.
For the triangle on the right side, the base is 8 - 4 = 4 centimeters and the height is 2 centimeters.
So, the area of the right triangle is: 0.5 * 4 * 2 = 4 cm^2.
Finally, we find the area of the rectangle. The length of the rectangle is 4 centimeters (the length of the right side of the trapezoid), and the width is 2 centimeters (the height of the trapezoid).
So, the area of the rectangle is: 4 * 2 = 8 cm^2.
Add the areas of the two triangles and the rectangle to find the total area of the trapezoid: 6 + 4 + 8 = 18 cm^2.
Therefore, the area of the trapezoid is 18 cm^2.
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