## anonymous one year ago What is the area of the figure?

1. anonymous

2. anonymous

@Nnesha

3. mathstudent55

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

4. mathstudent55

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5. mathstudent55

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

6. anonymous

polygon B looks like a triangle almost

7. trwatkins1

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

8. anonymous

lol its fine @trwatkins1

9. mathstudent55

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

10. mathstudent55

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?

11. anonymous

it seems to look like a slanted rhombus

12. mathstudent55

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13. trwatkins1

14. anonymous

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

15. mathstudent55

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

16. mathstudent55

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

17. anonymous

ok . lets take shot :)

18. mathstudent55

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

19. mathstudent55

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.

20. mathstudent55

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21. mathstudent55

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.

22. anonymous

so 12 * 24 which equals 288 , correct?

23. mathstudent55

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

24. anonymous

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

25. mathstudent55

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.

26. mathstudent55

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27. anonymous

28. mathstudent55

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.

29. trwatkins1

30. anonymous

I got 561.6 for the answer

31. mathstudent55

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

32. trwatkins1

math is that correct because thats what i got too

33. mathstudent55

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

34. trwatkins1

oh i did that wrong

35. trwatkins1

*facepalm

36. mathstudent55

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

37. anonymous

ooooh i did too , ok thanks !

38. mathstudent55

@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

39. mathstudent55

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.

40. anonymous

ok! thanks so much