Question

another question on the attachment :') i feel like such a pain for all the maths genius'!

Answer 1

\[\frac{\text{area of ADP}}{\text{area of ABCD}} \times 100\]

Answer 2

Trapezium...never heard that one. To solve, you only need DP and DC, which you can find with bit of trig:

\[DP = 5\tan(\frac{\pi}{6}) =\frac{5\sqrt{3}}{3}\]
\[DC = DP + \frac{5}{\tan(\frac{\pi}{9})} = DP + 13.73\]

From there, just compute the areas of the trapezium (trapezoid?) and the area of the shaded triangle, and find the percentage.

Answer 3

why do i need pi?

Answer 4

You don't need to use trig for this

Answer 5

Find the sum of the areas of the right triangles....that is all

Answer 6

but i dont know the lengths of any of the sides

Answer 7

Yeah, you need the side lengths for the areas.

Answer 8

i dont know what DC is

Answer 9

Yeah, okay, well use trig, but you don't need pi

Answer 10

I put the angles in radians, because radians are cooler. Just my preference, not a big deal.

Answer 11

ohh okay :') i dont know what that is haha sorry but thanks anyway!

Answer 12

Just substitute 180 degrees wherever you see pi...it's just another way of writing angles.

Answer 13

Why use radians when you don't have to?

Answer 14

I assumed it wouldn't be a big deal if the problem already involves some trig.

Answer 15

ohh okaythankssss

Answer 16

i cant do it :(

Answer 17

Ok, walk through it: first you need the area of the shaded triangle (ADP). That's \[\frac{1}{2}*5*DP\] (from the formula for the area of a triangle. Angle DAP is 30 degrees, so DP/5 = tan(30). A calculator will give you 2.88 for DP. That makes the area of ADP 7.216.

Answer 18

The area of the trapezoid is a little harder. You need to find the average of AB and DC, because that's how we find the area of trapezoids. We know that \[\tan(20) = \frac{5}{PC} \]
and thus, PC = 13.73. We can add this to ADP for a total length of 16.61 for DC. That makes the average of the bases 9.75, and so the area of the trapezoid is 5*9.75 = 48.725. Thus, the percentage of ABCD that is shaded is \[ 100*\frac{7.216}{48.725} \] or 14.8%.

Answer 19

Do you understand?

Answer 20

hang on let me just work it out :')

Answer 21

where did you get the average of the bases from?

Answer 22

Sorry, got disconnected for some reason...it's \[ \frac{AB+DC}{2} \]