What is the area of the figure?

Question

anonymous · Answer

attachment

anonymous · Answer

@Nnesha

mathstudent55 · Answer

You have two polygons in the figure.
Do you know what are the names of the two polygons?

mathstudent55 · Answer

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mathstudent55 · Answer

What type of polygon is polygon B?
Hint: It has three sides.

anonymous · Answer

polygon B looks like a triangle almost

trwatkins1 · Answer

btw the formulla is lenth x whith x hieght my grammer is bad

anonymous · Answer

lol its fine @trwatkins1

mathstudent55 · Answer

Exactly.
Polygon B is a triangle. To find its area we will use the formula for the area of a triangle.

mathstudent55 · Answer

Now we need to find out about polygon A.
You can see it has 4 sides. Each set of two opposite sides has the same length.
Do you know what polygon A is?

anonymous · Answer

it seems to look like a slanted rhombus

mathstudent55 · Answer

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trwatkins1 · Answer

bella the answer to a?

anonymous · Answer

you mean for the options ? there aren't any , this is o ne of the questions where you don't lol

mathstudent55 · Answer

It is close to a rhombus in certain way, but a rhombus has all sides of equal length.
Polygon A is a parallelogram.

mathstudent55 · Answer

Now we need to find the formulas for the area of a parallelogram and the area of a triangle.

anonymous · Answer

ok . lets take shot :)

mathstudent55 · Answer

$\large A_{parallelogram} = bh$

$\large A_{triangle} = \dfrac{bh}{2} $

mathstudent55 · Answer

The area of a parallelogram is the base times the height.
The base can be any side of the parallelogram. Once you choose a side as the base, then the height is a segment that goes from that base to the opposite side and is perpendicular to both sides.

mathstudent55 · Answer

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mathstudent55 · Answer

In your figure, we see that we can choose the side of 24-yd length to be the base. Then the height is the 12-yd dashed segment. Since we have a base and a height, we can find the area of the parallelogram.

anonymous · Answer

so 12 * 24 which equals 288 , correct?

mathstudent55 · Answer

Yes, for the parallelogram.
Now we look at the triangle below.

anonymous · Answer

ok I was thinking to do 15 * 8.4  which equals 126 , do we do that or what other should we do

mathstudent55 · Answer

We need a base and a height for the formula.
Any side of a triangle can be a base. Then the height is the length of a segment that is perpendicular to the base and ends in the opposite vertex.

mathstudent55 · Answer

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anonymous · Answer

ok I got the answer already!

mathstudent55 · Answer

Now that we see we can use the side of length 24 yd to be that base and the 8.4-yd side as the height, we use the formula for the area of a triangle.

$\large A = \dfrac{bh}{2} $

We multiply together the base and the height and we divide by 2.

trwatkins1 · Answer

bella whats the answer?

anonymous · Answer

I got 561.6 for the answer

mathstudent55 · Answer

15 yd is not a dimension of the triangle. It is the side of the parallelogram.

trwatkins1 · Answer

math is that correct because thats what  i got too

mathstudent55 · Answer

Total area = area of parallelogram + area of triangle =

$bh + \dfrac{bh}{2} = 24 \times 12 + \dfrac{24 \times 8.4}{2} $

$= 288 + 100.8 = 388.8 ~yd^2$

trwatkins1 · Answer

oh i did that wrong

trwatkins1 · Answer

*facepalm

mathstudent55 · Answer

The final answer is that the area of the figure is 388.8 square yards.

anonymous · Answer

ooooh i did too , ok thanks !

mathstudent55 · Answer

@Bella111 
Be careful with the area of the triangle.
Use base 24 yd and height 8.4 yd.
Multiply the base by the height and divide by 2.
Area of triangle = (24 yd * 8.4 yd)/2 = 100.8 yd^2

mathstudent55 · Answer

Then when you add the area of the triangle, 100.8, to the area of the parallelogram, 288, you get the total area of 388.8 sq yd.

anonymous · Answer

ok! thanks so much