area of sector help

http://www.ocr.org.uk/download/pp_11_jan/ocr_61408_pp_11_jan_gce_475201.pdf
question 9

area of sector=1/2r^2 theta

so area of sector= 1/2r^2 times pie/6 radians

so area of sector= pie/12 times r^2

then i dont know what to do. I need the triangle but in the marked solutions have they done the cosine rule?

First of all, this question is about cake not pie (seriously though - it's pi)

Second: You're doing right so far. That's the area of the whole slice. Now you need to work out the area of the triangle that's cut. Once you have that you know area of triangle must = 1/2 area of sector

http://www.ocr.org.uk/download/pp_11_jan/ocr_61408_pp_11_jan_gce_475201.pdf
question 9

area of sector=1/2r^2 theta

so area of sector= 1/2r^2 times pie/6 radians

so area of sector= pie/12 times r^2

then i dont know what to do. I need the triangle but in the marked solutions have they done the cosine rule?

triangle=1/2r^2theta

so i got it as 1/4r^2 but on mark scheme it says its 1/4a^2

oh wait dw is it because the radius is a

The area of triangle can be found using the formula, $\displaystyle \frac12 ab sinC$

So in this question it becomes, $\displaystyle \frac12 \times a \times a \times sin \frac{\pi}{6} = \frac12 \times a^2 \times sin \frac{\pi}{6}$


In this question the AREA OF SECTOR = 2 X AREA OF TRIANGLE.

'a' is not the radius.

Do a triangle has a radius?

'a' is the length of the sides.

'a' is not the radius.

Do a triangle has a radius?

'a' is the length of the sides.

area of triangle is also = 1/2r^2sin*theta

area of triangle is also = 1/2r^2sin*theta

I think you need to watch this video to first understand the formula.

Area of sector = $\dfrac{1}{2}r^2 \theta = \dfrac{1}{2}r^2(\frac{\pi}{6})$

Area of triangle = $\dfrac{1}{2}ab \sin C = \dfrac{1}{2}a^2(\sin (\frac{\pi}{6}))$ and since sin(pi/6) = 1/2 then this = $\dfrac{1}{4}a^2$

Also, the area of the triangle = 1/2 Area of sector. Solve for a.

ok, but the area of a triangle is also 1/2r^2sintheta it says it in my book

ok, but the area of a triangle is also 1/2r^2sintheta it says it in my book

Did you watched the video?

What is r? That is only true for isosceles triangles if r is the length of two equal sides of a triangle.

ok, but the area of a triangle is also 1/2r^2sintheta it says it in my book

and i got the same answer using that- 1/4a^2

What is r? That is only true for isosceles triangles if r is the length of two equal sides of a triangle. (i.e. yes it works for this question but that isn't the general area of a triangle formula)

It should give $\dfrac{a^2}4$, but i was suggesting to watch so that you understand the formula.

The are of sector was, $\dfrac{\pi r^2}{12}$

AREA OF SECTOR = 2 X AREA OF TRIANGLE.

$\displaystyle \dfrac{\pi r^2}{12} = 2 \times \dfrac{a^2}4$

yes okay so i could use that formula

area of triangle=1/2absinc

but why do i times it by 2 charlie wants to give half the slice to his m8