Question

Find the perimeter and area of the figure if each unit on the graph measures 1 centimeter. Round answers to the nearest tenth, if necessary.

Answer 1

The perimeter of the figure is approximately 22.4cm and the area of the figure is 26 square units.

The perimeter of a geometric figure is the total length of its boundary. In this case, the figure has four vertices labeled A, B, C, and D. To calculate the perimeter, we use the distance formula, which determines the distance between two points in a coordinate system.

For each side of the figure:

Length of AB: Calculate the distance between points A(-2,7) and B(4,4).

Length of BC: Calculate the distance between points B(4,4) and C(2,0).

Length of CD: Calculate the distance between points C(2,0) and D(-4,3).

Length of DA: Calculate the distance between points D(-4,3) and A(-2,7).

After finding the lengths of these sides, sum them up to obtain the perimeter. The formula for the distance between two points (x1​,y1​) and (x2,y2) is given by:

Distance=
`√((x2-x1)^2-(y2-y1)^2)`

By applying this formula to each side and adding the results, we get the total perimeter of the figure. In this specific case, the rounded perimeter is approximately 22.4cm.

Let's use the Shoelace Formula to find the area of the figure with vertices A(-2,7), B(4, 4), C(2, 0), and D(-4, 3):

Area= 1/2 ∣(−2×4)+(4×0)+(2×3)+(−4×7)−(7×4)−(4×2)−(0×(−4))−(3×(−2))∣

Now, calculate the expression inside the absolute value brackets and divide by 2:

Area= 1/2 ∣(−8+0+6−(−28)−28−8+0+6)∣

Area= 1/2 ∣(−52)∣

Area=26

Therefore, the area of the figure is 26 square units.