What is the area of the figure?

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What is the area of the figure?

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

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|dw:1441047382462:dw|
What type of polygon is polygon B? Hint: It has three sides.
polygon B looks like a triangle almost
btw the formulla is lenth x whith x hieght my grammer is bad
lol its fine @trwatkins1
Exactly. Polygon B is a triangle. To find its area we will use the formula for the area of a triangle.
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?
it seems to look like a slanted rhombus
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bella the answer to a?
you mean for the options ? there aren't any , this is o ne of the questions where you don't lol
It is close to a rhombus in certain way, but a rhombus has all sides of equal length. Polygon A is a parallelogram.
Now we need to find the formulas for the area of a parallelogram and the area of a triangle.
ok . lets take shot :)
\(\large A_{parallelogram} = bh\) \(\large A_{triangle} = \dfrac{bh}{2} \)
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.
|dw:1441047975610:dw|
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.
so 12 * 24 which equals 288 , correct?
Yes, for the parallelogram. Now we look at the triangle below.
ok I was thinking to do 15 * 8.4 which equals 126 , do we do that or what other should we do
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.
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ok I got the answer already!
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.
bella whats the answer?
I got 561.6 for the answer
15 yd is not a dimension of the triangle. It is the side of the parallelogram.
math is that correct because thats what i got too
Total area = area of parallelogram + area of triangle = \(bh + \dfrac{bh}{2} = 24 \times 12 + \dfrac{24 \times 8.4}{2} \) \(= 288 + 100.8 = 388.8 ~yd^2\)
oh i did that wrong
*facepalm
The final answer is that the area of the figure is 388.8 square yards.
ooooh i did too , ok thanks !
@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
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.
ok! thanks so much

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