Thread: Sat

hi,

my name is sara ...

I,m 15

and i has a sat test today

please

help me in this question

>>>>>>>>>>>>>>>><<<<<<<<<<<<<<<<<<<<<


in the figure at the right.
the legs of right tringle ACB are diameters of the two semicircles. If AB=4 ,What is the sum of the areas of the semicircles?



(a) 3.14 (b) 2 x 3.14 (c) 4 x 3.14 (d) 8 x 3.14 (c) 16 x 3.14


please help me.....

Assume it is an isosceles triangle and therefore D^2 + D^2 = 4^2

solve for D and you will find one leg of the triangle or the diameter of the semicircle.

The area of the semi circle will be

1/2*(Pi*(D/2)^2) and since you have two of them you will find the sum of the area is:

Pi*(D/2)^2

so, What is the answer??


(( sorrry i am not good in english because english is not my mother language))

D^2 + D^2 = 4^2

2(D^2) = 16

D^2 = 8

D = Sqrt(8)

can you do the rest?

Here is the rest:

Given:
Area= Pi*(D/2)^2 and D=sqrt(8)



Area= Pi*(sqrt(8)/2)^2

Area= Pi*(8/4)

Area= 2*Pi

so B is the answer

Thank you

i hope i get a good mark in SAt text

Your welcome,

always try to understand what you are doing rather than just focus on the answer. Please tell your friends in Qatar about this website, I hope you found it useful.

Cheers,

how do you know that i am from Qatar?

Originally Posted by MathGuru

Assume it is an isosceles triangle and therefore D^2 + D^2 = 4^2

solve for D and you will find one leg of the triangle or the diameter of the semicircle.

The area of the semi circle will be

1/2*(Pi*(D/2)^2) and since you have two of them you will find the sum of the area is:

Pi*(D/2)^2

No assumptions are needed the areas of the semi-circles obey a semi-circle
version of Pythagoras's theorem.

The area of the semi-circle on the hypotenuse of a right triangle is equal
to the sum of the areas of the semi-circles on the other two sides.

Hence the sum of the areas of the two semi-circles shown is equal to
the area of a semi-circle on the hypotenuse, which is:



RonL

Thanks Ron for the correction.

Sara I checked your IP address which show that you are in Qatar.