Area and Volume Q

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I am having a problem figuring this one out. I have found the area of the trapezium to be 96 and then got the area of the triangle 30 after using pythagoras.I the put 66/96 and times 100 to get percentage of 66.75%. The back of the book goves 81.25% however.

Bruthal

Im getting 81.25 for some reason.

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robbie7730 wrote: »

Im getting 81.25 for some reason.

Sorry it is 81.25 actually. Can you tell me how you got it? I know I am making a glaring mistake somewhere

Bruthal

Well you got the total area as 96, which I did by making the left section into a triangle as well as the shaded right side, with a rectangle in the middle.

Not having done much maths in a long time, this is what I did

Left triangle now has a known side of 13, and the line added to make it a triangle perpendicular to the bottom of the trapezium is 12 long as given in drawing.

Pythagoras
13 x 13 = 169. 12 x 12 = 144
169 - 144 = 25 so the bottom of that triangle is now root 25 = 5

So area of this triangle = 5 x 12 / 2 = 30

Bottom of trapezium is 12. - the 5 = 7. - the 4 for the top of rectangle middle section which is same as bottom = 3 which is now the length of the bottom of the yellow triangle.

Yellow triangle area = 3 x 12 / 2 = 18

Rectangle section = 4 x 12 = 48

So I added the 18 to the first triangle and the centre rectangle = 18+30+48 = 96

Area without the yellow triangle = 96-18 = 78

78 / 96 x 100 = 81.25

locum-motion

Drop a vertical from the upper left corner.
The area of the triangle to the left of this vertical is 30.
However, the area of the yellow triangle isn't 30, it's 18.