Question

This figure is made up of a rectangle and parallelogram. What is the area of this figure? Enter your answer in the box. Do not round any side lengths. units² Coordinate plane with axes labeled x and y. A closed figure is formed by a parallelogram and rectangle. The vertices are negative 10 comma 2, negative 7 comma 3, negative 1 comma 3, 1 comma negative 3, negative 2 comma negative 4, and negative 4 comma 2.

Answer 1

To find the area of the figure, we need to find the area of the rectangle and the area of the parallelogram, and then add them together.

First, we need to identify which sides of the figure belong to the rectangle and which sides belong to the parallelogram. Looking at the coordinates of the vertices, we can see that the vertices (-10,2), (-7,3), (-1,3), and (1,-3) form a parallelogram, while the vertices (-7,3), (-2,-4), and (-4,2) form a rectangle.

To find the area of the parallelogram, we can use the formula:

Area = base × height

where the base is the length of one of the sides of the parallelogram, and the height is the perpendicular distance between the base and the opposite side. We can choose any side of the parallelogram as the base, but it is usually easiest to choose the side that is perpendicular to the x-axis, since its length is simply the difference between the x-coordinates of the two endpoints.

Using the coordinates (-10,2) and (-7,3) as the endpoints of the base, we find that the length of the base is:

|-7 - (-10)| = 3

To find the height, we need to find the perpendicular distance between the base and the opposite side of the parallelogram. We can do this by drawing a vertical line from one endpoint of the base to the opposite side, and then measuring the length of this line. We can see that the line from (-10,2) to (-1,3) is perpendicular to the base, so its length is the height of the parallelogram:

|-1 - (-10)| = 9

Therefore, the area of the parallelogram is:

Area = base × height = 3 × 9 = 27

To find the area of the rectangle, we simply need to multiply the length and width of the rectangle. We can see that the length is the distance between (-7,3) and (-4,2):

|-4 - (-7)| = 3

and the width is the distance between (-7,3) and (-2,-4):

|(-2) - (-7)| = 5

Therefore, the area of the rectangle is:

Area = length × width = 3 × 5 = 15

Finally, we can find the area of the whole figure by adding the area of the rectangle and the area of the parallelogram:

Area of figure = Area of rectangle + Area of parallelogram

= 15 + 27

= 42

Therefore, the area of the figure is 42 square units.