E maths question

bonkysleuth SG

The diagram shows a picture grame ABCDE which consists of a rectangle ABCE and an arc CDE with centre O. The diagonals of the rectangle intersect at O.

Calculate the area of the picture frame ABCDE.

Looks easy but my answer differs from the answer booklet. I got 167cm2 (something like that) but answer is 157cm2. Checked it numerous times but still can't spot the error. Please help take a look. (:

wee_ws SG

Hi,

Perhaps you could post your working for us to check and comment. Thanks!

Cheers,
Wen Shih

bonkysleuth SG

Hi,

Perhaps you could post your working for us to check and comment. Thanks!

Cheers,
Wen Shih

Oh, hi! Here's taking a look at what I did.

Area of picture frame = 0.5 X 1 X 8 + 0.5 X 8 X 7.5 + (0.5 X 8.5^2 X 2.16678001)

=168.0906cm2

For which the 2.1616 is the angle of COE in radians. Firstly I used the formula for finding the trangle on the left hand side. Now you're left with the smaller triangle on RHS with a breadth of 8cm and 7.5cm in length(which is derived by dividing 2 from 15). The 3rd addition is from the area of the sector given by 0.5r^2theta.

Spot any mistakes? (though I hope it isn't my mistake. Hope so.) ;p

dkcx SG

I hate combine working cos its hard to check but i assume (0.5 X 8.5^2 X 2.16678001) is the area of the sector. Why did you use 8.5 as the radius? Is the length of CO 8.5? That might be where you went wrong.

wee_ws SG

Hi,

Note that OC is 1/2 AC and AC can be found by Pythagoras' Theorem.

As for angle COE, note that triangle COE is isosceles and its base angles are arctan(8.5/15).

Finally, once we found the area of sector, we just need to compute the three smaller triangles. Thanks for pointing out the error, dkcx!

Cheers,
Wen Shih

dkcx SG

Hi,

Note that OC is 1/2 AC and AC can be found by Pythagoras' Theorem.

As for angle COE, note that triangle COE is isosceles and its base angles are arctan(8.5/15).

Finally, once we found the area of sector, we just need to compute 75% of the area of rectangle to complete the working.

Thanks!

Cheers,
Wen Shih

Since this is a reactangle, i don't think its 75% of the area since the triangles are not exactly equal in size due to the difference in length and breath so he will still need to find the area of the triangle that is part of the sector to get his answer.

bonkysleuth SG

Hi thanks everyone!

Will like to say that the 8.5 cm and the value for angle COE are correct, 8.5 cm and 2.162 respectively. This is because there is an earlier portion(which is in another page) that requires me to prove them and I forgot to post it up. Sorry!

Eh, sorry to say, but I still don't know my error. >.<

TenSaru SG

I think you saw the diagram wrongly... All the values that are supposed to be 8.5 have become 8 in your working

dkcx SG

I think you saw the diagram wrongly... All the values that are supposed to be 8.5 have become 8 in your working

If the values use 8.5 instead of 8, the final ans would be larger and even further from the given answer if TS did use 8 instead of 8.5 to do his calculations.

Darkness_hacker99 SG

This is my approach. Please give some comment =S

wee_ws SG

Hi,

Thanks for your worked solution. I obtained the same value too.

Cheers,
Wen Shih