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Advocard [28]
3 years ago
12

A parallelogram is shown below: Part A: What is the area of the parallelogram? Show your work. (5 points) Part B: How can you de

compose this parallelogram into two triangles? If this parallelogram was decomposed into two triangles, what would be the area of each triangle?

Mathematics
2 answers:
kirill115 [55]3 years ago
8 0

Answer:

<u><em>Part A) Area of Parallelogram:</em></u>

Area = Base*Height

Area = 3 * \frac{2}{3}

<u><em>Area = 2 feet²</em></u>

<u><em>Part B)</em></u>

We can  decompose the parallelogram into two triangle by drawing a diagonal which will divide the parallelogram into two triangles with equal area

<u><em>Part C)</em></u>

The area of each triangle would be the half of the area of parallelogram.

=> <u><em>Area of each triangle = 2 feet²/2 = 1 feet ²</em></u>

aksik [14]3 years ago
5 0

Part A) The area of a parallelogram is base × height.

3 × 2/3 = 6/3 = 2

2 feet squared is the area of the whole parallelogram.

Part B) The diagonal of a parallelogram separates it into two congruent triangles.

The area of each triangle will be:

base × height × 1/2

3 × 2/3 × 1/2 = 6/6 = 1

1 foot squared is the area for each triangle.

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The average heights of x number of girls and 15 boys is 123. if the average heights of boys is 125 and that of girls is 120.find
mamaluj [8]

Answer:

x = 10. In other words, there number of girls is 10.

Step-by-step explanation:

The average of a number of measurements is equal to the sum of these measurements over the number of measurements.

\displaystyle \text{Average} = \frac{\text{Sum of measurements}}{\text{Number of measurements}}.

Rewrite to obtain:

\begin{aligned}& \text{Sum of measurements}= (\text{Number of measurements}) \times (\text{Average}) \end{aligned}.

For this question:

\begin{aligned}& \text{Sum of heights of boys} \\ &= (\text{Number of boys}) \times (\text{Average height of boys}) \\ &= 15 \times 125 = 1875\end{aligned}.

\begin{aligned}& \text{Sum of heights of girls} \\ &= (\text{Number of girls}) \times (\text{Average height of girls}) \\ &= x \times 120 = 120\, x\end{aligned}.

Therefore:

\begin{aligned}& \text{Sum of boys and girls} \\ &= \text{Sum of heights of boys} + \text{Sum of heights of girls}\\ &= 1875 + 120\, x\end{aligned}.

On the other hand, there are (15 + x) boys and girls in total. Using the formula for average:

\begin{aligned}& \text{Average height of boys and girls} \\ &= \frac{\text{Sum of heights of boys and girls}}{\text{Number of boys and girls}} \\ &= \frac{1875 + 120\, x}{15 + x}\end{aligned}.

From the question, this average should be equal to 123. In other words:

\displaystyle \frac{1875 + 120\, x}{15 + x} = 123.

Solve this equation for x to obtain:

1875 + 120\, x= 123\, (15 + x).

(123 - 120)\, x = 1875 - 123 \times 15.

x = 10.

In other words, the number of girls here is 10.

5 0
3 years ago
Help me please <br><br> Love you, thanks!!!
balu736 [363]

Answer:

Neither for 1

the second option for 2

Step-by-step explanation:

not sure how to explain this

8 0
3 years ago
Read 2 more answers
Which Pairs are additive inverses?<br> a. 6,-(-6)<br> b. -7,7<br> c.-7,-7<br> d.7,7<br> e.6,-6
xz_007 [3.2K]

I was never sure of what the "additive inverse" is. 
So, just now, just for you, I went and looked it up.

The additive inverse of any number ' A ' is the number
that you need to ADD to A to get zero.  That's all !

So now, let's check out the choices:

a), 6, -(-6)

That second number, -(-6), is the same as +6 .
So the two numbers are the same.
Do you get zero when you add them up ?  No.

b). -7, 7
What do you get when you add -7 and 7 ?
You get zero.
So these ARE additive inverses.

c). -7, -7
What do you get when you add -7 to -7 ?
You get -14 .  That's not zero, so these
are NOT additive inverses.

d).  7, 7
What do you get when you add 7 to 7 ?
You get 14.  That's NOT zero, so these
are NOT additive inverses.

e).  6, -6
What do you get when you add 6 to -6 ?
You get zero.
So these ARE additive inverses.

What do we end up with from the list of choices:

a).,  c).,  and d). are NOT additive inverses.

b). and e). ARE additive inverses.

7 0
3 years ago
Read 2 more answers
What's the answer to number 3
Evgesh-ka [11]
Do you know what you need to do to solve this problem?
3 0
3 years ago
5.
irina [24]

Answer:

160 m²

384 m²

Step-by-step explanation:

The area of a trapezium is given by :

A = 1/2(a + b)h

h = height ; a and b = lengths

From the diagram :

A = 1/2(12 + 20)10

A = 1/2(32)10

A = 16 * 10

A = 160 m²

2.)

Area of parallelogram = base * height

Base = 24 ; h = 16

A = 24 * 16

A = 384 m²

7 0
3 years ago
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