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hellooooo im having some trouble with a problem... I'm really bad at geo and im sorry for wasting your time, but i really need someone to walk me through:

 

Each vertex of this parallelogram has integer coordinates. The perimeter of this parallelogram is $p$ units, while the area is $a$ square units. What is the value of the sum $p + a$?

 

thank you so much!!! :D

 Jul 28, 2021
 #1
avatar+54 
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Ok. So we know the perimeter, because we know two coordinates. That is because this is a parallelogram, meaning opposite sides are equal length. We can see the bottom side is just 7 units long, and that the top side is also 7 units. We have 2 of the sides, meaning weshould get the slanted sides now. We use the pythagorean theorem for it, and know that the we want \(\sqrt{x^2+y^2}=\) slanted side. We set x to the base, and y to the leg. x is 3, because it coincides with the upper point, (3,4), but with y is 0. That means x is 3, and y is 4. That is just the lengths of the triangle, and once we plug it in, we get sqrt(25). That is 5, so we have our perimeter. Our perimeter is 5+5+7+7, which is 24. The area, I split up the parallelogram into 2 same triangles, and a rectangle in the middle. For the two triangles, it is just 3*4*(1/2), that means 6 and another 6. The middle, is just a 4 times 4 square, which has an area of 16. Therefore,  the area is 28. That means, for te perimeter + area, is 52.

 Jul 28, 2021
 #2
avatar+34313 
+2

Area = height * base = 4 x 7 = 28 = a

Perimeter = 7 + 7 + 5 + 5 = 24 =p      because the side triangles form a 3 - 4 - 5 right triangle

   Add them together to get 52 units

 Jul 28, 2021
 #3
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+1

thank you so much!! i had to read through a few times to understand... but this was really helpful!! :)))

 Jul 28, 2021

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