On a graph, the points (4,-2),(7,-2),(9,-5) and (2,-5) are connected in order to form a trapezoid. To the nearest tenth, what is its perimeter?
In order to figure the length of a line segment, you have to rely on the Pythagorean Theorem. If that doesn't sound familiar, you need to review your text. The theorem states that in a right triangle with legs a and b, with hypotenuse c,
c2 = a2 + b2
Now, if you plot two points on a piece of graph paper, such as (7,-2) and (9,-5), the line joining the points will be a slanting line. If you draw horizontal and vertical lines from each point, they will intersect to form a right triangle. The length of the legs are just the x-distance from 7 to 9 = 2, and the y-distance from -5 to -2 = 3.
So, the length of the hypotenuse is given by
h2 = 22 + 32
h2 = 13
so,
h = √13
If you follow these steps for each side of the figure, you can add up all the lengths to get the perimeter.
Thank you for your help, I still don't understand
To find the perimeter of a trapezoid, we need to calculate the sum of the lengths of its four sides.
Let's calculate the lengths of the sides by finding the distances between each pair of consecutive points.
First, calculate the length of the bottom side of the trapezoid using the coordinates (4,-2) and (7,-2):
Length of the bottom side = √[(x2 - x1)^2 + (y2 - y1)^2]
= √[(7 - 4)^2 + (-2 - (-2))^2]
= √[(3)^2 + (0)^2]
= √[9 + 0]
= √9
= 3
Next, calculate the length of the right side of the trapezoid using the coordinates (7,-2) and (9,-5):
Length of the right side = √[(x2 - x1)^2 + (y2 - y1)^2]
= √[(9 - 7)^2 + (-5 - (-2))^2]
= √[(2)^2 + (-3)^2]
= √[4 + 9]
= √13
Then, calculate the length of the top side of the trapezoid using the coordinates (9,-5) and (2,-5):
Length of the top side = √[(x2 - x1)^2 + (y2 - y1)^2]
= √[(2 - 9)^2 + (-5 - (-5))^2]
= √[(-7)^2 + (0)^2]
= √[49 + 0]
= √49
= 7
Finally, calculate the length of the left side of the trapezoid using the coordinates (2,-5) and (4,-2):
Length of the left side = √[(x2 - x1)^2 + (y2 - y1)^2]
= √[(4 - 2)^2 + (-2 - (-5))^2]
= √[(2)^2 + (3)^2]
= √[4 + 9]
= √13
Now, let's sum up the lengths of all four sides of the trapezoid:
Perimeter = Length of bottom side + Length of right side + Length of top side + Length of left side
= 3 + √13 + 7 + √13
≈ 3 + 3.6 + 7 + 3.6
≈ 17.2
Therefore, to the nearest tenth, the perimeter of the given trapezoid is approximately 17.2 units.
Compute the four side lenghts using the pairs of coordinates.
The side that goes from (4,-2) to (7,-2) has a length of sqrt[(7-4)^2 + (2 -(-2)^2] = 5
Do the others the same way.
Then add all four.