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
A 75 cm^2
B 100 cm^2
C 125 cm^2
D 80 cm^2
B 100 cm^2
To find the area of a parallelogram, you can use the formula: Area = base x height. In this case, the base can be considered as the top side (5 cm) and the height can be considered as the dotted perpendicular line (4 cm).
So, Area = 5 cm x 4 cm = 20 cm^2. However, because a parallelogram is made up of two congruent triangles, we need to calculate the area of one of those triangles and then double it.
The area of the triangle can be calculated using the formula: Area = 1/2 x base x height. In this case, the base is the side length of the parallelogram, which is 5 cm, and the height is the perpendicular line, which is 4 cm.
Therefore, Area of one of the triangles = 1/2 x 5 cm x 4 cm = 10 cm^2
And since the parallelogram is made up of two congruent triangles, the total area of the parallelogram is 2 x 10 cm^2 = 20 cm^2.