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
100 cm2
100 cm squared
125 cm2
125 cm squared
80 cm2
80 cm squared
75 cm2
75 cm squared
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To find the area of the quadrilateral, we can split it into two triangles by drawing a perpendicular line from the top left vertex to the bottom side. This will create two right triangles.
The area of a triangle is calculated using the formula: 1/2 * base * height.
First, calculate the area of the left triangle:
Base = 5 cm
Height = 4 cm
Area = 1/2 * 5 * 4 = 10 cm^2
Now, calculate the area of the right triangle:
Base = 25 cm
Height = 4 cm
Area = 1/2 * 25 * 4 = 50 cm^2
Add the areas of the two triangles together to get the total area of the quadrilateral:
10 cm^2 + 50 cm^2 = 60 cm^2
Therefore, the correct answer is 60 cm^2.
what is the answer
Apologies for the mistake in my previous response. Let me correct it.
To find the area of the quadrilateral, we can use the formula for the area of a trapezoid: 1/2 * (sum of the bases) * height.
In this case, the two bases are the top side and the bottom side. The top side is 5 cm, and the bottom side can be calculated by Pythagorean theorem:
Bottom side = sqrt(25^2 - 4^2) = sqrt(625 - 16) = sqrt(609) ≈ 24.65 cm
Now, we can calculate the area of the quadrilateral:
Area = 1/2 * (5 + 24.65) * 4 = 1/2 * 29.65 * 4 ≈ 59.3 cm^2
Therefore, the correct answer is approximately 59.3 cm^2.