Use the image to answer the question.
An illustration shows a parallelogram with top side as 7 centimeters. A perpendicular dotted line from the top left vertex to the bottom side is 12 centimeters. The perpendicular line makes one right angle symbol with the top side and two right angle symbols with the bottom side.
What is the area of the quadrilateral?
(1 point)
cm2
Skip to navigation
The area of the quadrilateral can be calculated by finding the area of the triangle formed by the perpendicular line and the bottom side, and subtracting it from the area of the parallelogram.
The area of the triangle = (1/2) * base * height
Area = (1/2) * 7 * 12 = 42 cm²
The area of the parallelogram = base * height
Area = 7 * 12 = 84 cm²
Therefore, the area of the quadrilateral is 84 cm² - 42 cm² = 42 cm².
wrong
I apologize for the mistake. Let's calculate the correct area of the quadrilateral.
Since the perpendicular line from the top left vertex divides the parallelogram into two right triangles and a rectangle, we can calculate the total area by finding the area of each individual shape and then summing them up.
Area of the rectangle = base * height = 7 cm * 12 cm = 84 cm²
Area of each right triangle = (1/2) * base * height
Area of each right triangle = (1/2) * 7 cm * 12 cm = 42 cm²
Since there are two right triangles, total area = 2 * 42 cm² = 84 cm²
Therefore, total area of the quadrilateral = 84 cm² (rectangle) + 84 cm² (two right triangles) = 168 cm²
So, the correct area of the quadrilateral is 168 cm².
Area of Special Quadrilaterals Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
3 of 53 of 5 Items
Question
Use the image to answer the question.
An illustration shows a parallelogram with top side as 7 centimeters. A perpendicular dotted line from the top left vertex to the bottom side is 12 centimeters. The perpendicular line makes one right angle symbol with the top side and two right angle symbols with the bottom side.
What is the area of the quadrilateral?
(1 point)
cm2
Skip to navigation
To find the area of the quadrilateral, we can divide it into two triangles and a rectangle. The rectangle's area is your standard base times height calculation, which in this case is 7 cm * 12 cm = 84 cm².
The two triangles each have an area of 1/2 * base * height. For each triangle, the base is 7 cm and the height is 12 cm. Therefore, the area of each triangle is 1/2 * 7 cm * 12 cm = 42 cm². Since there are two triangles, their combined area is 2 * 42 cm² = 84 cm².
Adding the area of the rectangle and the combined area of the triangles, we get:
84 cm² (rectangle) + 84 cm² (two triangles) = 168 cm²
Therefore, the area of the quadrilateral is 168 cm².