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3 years ago

What is the area of parallelogram ABCD? ____ square units

Mathematics

1 answer:

valentinak56 [21]3 years ago

6 0

Answer:

Step-by-step explanation:

Here's a method of finding the area of any polygon knowing its vertices. I'm using this parallelogram as an example.

Make a table like this (each vertex with its x- and y-coordinates):

Pt x y

A 3 6

B 6 5

C 5 1

D 2 2

A 3 6

Now multiply each x-coordinate by the y-coordinate on the line below and write it on the right side. Bold type shows the first multiplication.

x y

A 3 6

B 6 5 15

C 5 1 6

D 2 2 10

A 3 6 12

Now multiply each y-coordinate by the x-coordinate on the line below and subtract from each produce you already have. Do each subtraction. Bold type shows the first multiplication.

x y

A 3 6

B 6 5 15 - 36 = -21

C 5 1 6 - 25 = -19

D 2 2 10 - 2 = 8

A 3 6 12 - 6 = 6

Add all the differences.

x y

A 3 6

B 6 5 15 - 36 = -21

C 5 1 6 - 25 = -19

D 2 2 10 - 2 = 8

A 3 6 12 - 6 = 6

+____

-26

The area of the polygon is the absolute value of half of the sum of the differences.

area = |-26/2| = |-13| = 13

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Solution:

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Factorization is a method of writing numbers as the product of their factors or divisors.

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Factoring out the GCF:

This methods means that factoring out common factors

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The sum-product pattern

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The grouping method

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$2x^2 + 7x + 3\\\\2x^2 + 6x + 1x + 3\\\\2x(x + 3) + 1(x + 3)\\\\(x + 3)(2x + 1)$

The perfect square trinomial pattern

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3 years ago

Irina wants to build a fence around a rectangular vegetable garden so that it has a width of at least 10 feet. She can use a max

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Step-by-step explanation:

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3 years ago

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$y_p=u_1y_1+u_2y_2$

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$u_1=-\displaystyle\frac13\int\frac{y_2e^x\sec x}{W(y_1,y_2)}\,\mathrm dx$
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and $W(y_1,y_2)$ is the Wronskian of the fundamental solutions. We have

$W(e^x\cos x,e^x\sin x)=\begin{vmatrix}e^x\cos x&e^x\sin x\\e^x(\cos x-\sin x)&e^x(\cos x+\sin x)\end{vmatrix}=e^{2x}$

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