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2 years ago

What is the area of a parallelogram if the coordinates of its vertices are (0, -2), (3, 2), (8,2), and (5,-2)?

Mathematics

1 answer:

Llana [10]2 years ago

7 0

Answer:

The area of the parallelogram is 20 units²

Step-by-step explanation:

* Lets explain how to solve the problem

- The vertices of the parallelogram are (0 , -2) , (3 , 2) , (8 , 2) , (5 , -2)

- The side joining the points (0 , -2) and (5 , -2) is a horizontal side

because the points have same y-coordinates

- The side joining the points (3 , 2) and (8 , 2) is a horizontal side

because the points have same y-coordinates

∴ These two sides are parallel bases of the parallelogram

∵ The length of any horizontal side = x2 - x1

∴ The length of the side = 5 - 0 = 5 <em>or</em> 8 - 3 = 5

∴ The length of one base of the parallelogram is 5 units

- The height of this base is the vertical distance between these two

parallel bases

∵ The length of any vertical distance = y2 - y1

∵ y2 = 2 and y1 = -2 ⇒ the y-coordinates of the parallel bases

∴ The length of the vertical distance = 2 - (-2) = 2 + 2 = 4 units

∵ This vertical distance between the two parallel bases is the height

of these bases

∴ The height of the parallelogram is 4 units

- The area of the parallelogram = base × height

∵ The base = 5 units and the height = 4 units

∴ The area = 5 × 4 = 20 units²

* The area of the parallelogram is 20 units²

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2 years ago

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Answer:

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Step-by-step explanation:

<em><u>The correct question is </u></em>

If ABCD is a square and AB = 10, what is the measure of AC? (rounded to the nearest hundredth)

see the attached figure to better understand the problem

we know that

All four sides of the square are congruent and all four interior angles are equal to 90°.

AB=BC=CD=AD

In the right triangle ACD

Applying the Pythagorean Theorem

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