gcse answer check please

[12345678]

"calculate the area of the shaded shape, giving your answer in terms of pie". The question involved a triangle and a quarter of a circle. There was a right-angled triangle with 2 sides of 12cm (the hyp was unknown), with a quarter of a circle covering the hyp- so diameter of circle=hyp. Firstly, I worked out the hyp, using a^2+b^2=c^2. So 12^2+12^2=288. The hyp therefore= 12(squareroot sign)2. I then worked out the radius of the circle was half of 12(square root) 2 as r=diameter/2, so r=6(squareroot)2. To calculate the area, I did pie x (6(squareroot )2)^2/4. The answer was 18. As the answer was in terms of pie, I then multiplied 18 by pie, so the area was 18pie. However my textbook says the answer is 36pie-72. Can anybody tell me where I have gone wrong please. (ps sorry if it sounds confusing, I cant get a diagram).

 

[Deleted member 4993]

"calculate the area of the shaded shape, giving your answer in terms of pie". The question involved a triangle and a quarter of a circle. There was a right-angled triangle with 2 sides of 12cm (the hyp was unknown), with a quarter of a circle covering the hyp- so diameter of circle=hyp. Firstly, I worked out the hyp, using a^2+b^2=c^2. So 12^2+12^2=288. The hyp therefore= 12(squareroot sign)2. I then worked out the radius of the circle was half of 12(square root) 2 as r=diameter/2, so r=6(squareroot)2. To calculate the area, I did pie x (6(squareroot )2)^2/4. The answer was 18. As the answer was in terms of pie, I then multiplied 18 by pie, so the area was 18pie. However my textbook says the answer is 36pie-72. Can anybody tell me where I have gone wrong please. (ps sorry if it sounds confusing, I cant get a diagram).

Area of semicircle = π * d²/8 = π * (288)/8 = 36 * π

Area of the triangle = 1/2 * b * h = 72

Hence the total area = (Area of semicircle) - (Area of the triangle) = 36 * π - 72

 

[12345678]

Area of semicircle = π * d²/8 = π * (288)/8 = 36 * π

Area of the triangle = 1/2 * b * h = 72

Hence the total area = (Area of semicircle) - (Area of the triangle) = 36 * π - 72

Cheers for your reply, but there are a few things I don't understand. If you use the radius to find the area-(ill use "n" as pie), area=nr^2, so n x (6(square root)2)^2 gives you an answer of 72n. If it is a quarter circle, should you not divide by 4 to give 18n? Also, if it just wants the area of the shaded shape, why do you take away the area of the triangle?

 

[HallsofIvy]

It would be better if you could give a picture or at least describe the situation more precisely. You say "with a quarter of a circle covering the hyp- so diameter of circle=hyp". That sounds like a half circle or semi-circle.

 

[12345678]

It would be better if you could give a picture or at least describe the situation more precisely. You say "with a quarter of a circle covering the hyp- so diameter of circle=hyp". That sounds like a half circle or semi-circle.

There should be a picture attached to this reply

 

[Deleted member 4993]

There should be a picture attached to this reply

So then radius of your circle is 12

The area " included in the quarter circle - but not covered by the triangle " = π/4 *(12)² - 1/2*12*12 = 36*π - 72

 

[Bob Brown MSEE]

"calculate the area of the shaded shape, giving your answer in terms of pie". The question involved a triangle and a quarter of a circle. There was a right-angled triangle with 2 sides of 12cm (the hyp was unknown), with a quarter of a circle covering the hyp- so diameter of circle=hyp. Firstly, I worked out the hyp, using a^2+b^2=c^2. So 12^2+12^2=288. The hyp therefore= 12(squareroot sign)2. I then worked out the radius of the circle was half of 12(square root) 2 as r=diameter/2, so r=6(squareroot)2. To calculate the area, I did pie x (6(squareroot )2)^2/4. The answer was 18. As the answer was in terms of pie, I then multiplied 18 by pie, so the area was 18pie. However my textbook says the answer is 36pie-72. Can anybody tell me where I have gone wrong please. (ps sorry if it sounds confusing, I cant get a diagram).

AB=BC=12
AC = 12 Root(2)
r = 6Root(2)
rr = 2*36 = 72
Pi*r*r = Pi * 72

A = {Triangle} + {SemiC}
A = {(1/2)12*12} + {Pi * 72 /2}
A = 72 + 36 Pi