Area List

What is the area formula for a circle

A= pi* r^2
The area is equal to pi times the radius squared. If you do not have the radius, use the diameter. The radius is equal to the diameter divided by 2.

I don’t want someone to answer one of my geometry questions so im asking this. I totally forgot the formula for the area of a triangle. Help

a=bh
—–
2

a= 1/2bh

Either one should work.

Ok… lets make this easy. I want to know a trick to help me remember the formula for the circumference and area of a circle. The formula for circumference is C: 2 Pi r. (I’m really bad at memorizing things!) The formula for the area of a circle is A: Pi r squared. The squared is the little two. Whoever answers this first gets ten points!

I think if you get a tattoo of the formula on the back of your hand you’re golden.

What is surface area, dealing with math and what is an easy formula to find the surface area of a right circular cylinder?

surface area
let r be radius of base of cylinder
let h be height of cylinder
surface area of right circular cylinder
=2*(area of flat circular face/base)+ curved area
—–it has 2 flat circular faces
area of flat circular face
=pi*r*r

area of curved surface= circumfurence of base * height
= (2*pi*r) * h

therefore total surface area of a right circular cylinder= 2*pi*r*r + 2*pi*r*h

I hope u have understood the meaning of surface area as well.–roughly the total area of outer surface of an object

best regards,

I have to derive the trapezium rule. In other words going from h/2(a+b) (the formula to get the area of a trapezium) to h/2[f(0)+2(f(1)+f(2)+...+f(n-1))+f(n)] (the trapezium rule)

I really hope that makes sense…

Yes it makes sense. You are talking about finding areas under a curve numerically rather than by integration.

The first strip will have sides f(0) and f(1) so its area is
(h/2)[f(0) + f(1)]
The second strip has sides f(1) and f(2) so its area is
(h/2)[f(1) + f(2)]
Continue in this way up to the penultimate strip area of
(h/2)[f(n-2) + f(n-1)]
and the final strip with area of
(h/2)[f(n-1) + f(n)]

Adding these up you see that (h/2) is a common factor. All the function terms appear twice except f(0) and f(n) which only appear once. That is why the long bracket starts
f(0) + 2f(1) + 2f(2) . . .
and ends
. . . 2f(n – 2) + 2f(n – 1) + f(n)

P.S. You have missed out some of the 2’s in your long bracket.

Surface Area of a Sphere = 4 pi r 2

where r is the radius

Why is it side squared times 1.72 is the formula for finding the area of a regular pentagon?

Coorect girl!

Area of a regular pentagon = 1.72048 x side (squared)

This is the easier one where the length of the side is given! However, there is another formula that can be used.

The area of a pentagon is given by:
Area = (½)x(apothem)x(perimeter)

Perimeter = 5 x side
Apothem = radius of incribed circle (of the pentagon)

Such a formula is used to find the apothem, because from the perimeter, you can always find the side of the pentagon.
Enjoy!

1) the integral from 1/2 to 1 for sqrt(1- x^2)

2) The integral from 0 to 1 for sqrt (2 – x^2)

I know that the graph of these are circles and to use πr^2 but I don’t know how…? Thanks

Your teacher is being unnecessarily cruel by making you use the formula for the area of a circle to evaluate the integral. If you could argue that these are pie slices, it would be much easier, but they aren’t.

Look, the indefinate integral relative to x of sqrt(r^2 – x^2) is…
∫sqrt(r^2 – x^2) dx = 1/2*x^2*sqrt(r^2 – x^2) + 1/2*r^2*arctan(x/sqrt(r^2-x^2)) + C

Call this I(x) = 1/2*x^2*sqrt(r^2 – x^2) + 1/2*r^2*arctan(x/sqrt(r^2-x^2)) + C

Your arctangent function will return in radians, so have your mode set accordingly.

For part 1: r = 1. Plug in x=1 and x=1/2 to the indefinite integral result. Subtract I(1) – I(1/2) and you got your result. We do need to replace the arctangent function with Pi/2, because it is the arctangent of an expression containing division by zero. 0.8307 units^2 is the answer. The analytical answer is a mess, so no need to show.

For part 2: r = sqrt(2). Plug in x=1 and x=0 to the indefinite integral result. Subtract I(1) – I(0) and you got your result. 1/2 + Pi/4 gives you the answer, or 1.285 units^2.

I need to find surface area for a cone… and I need the formula.

Thanks!
(Please hurry and answer, I need my good sleep and need to hit the hay soon!)

π*r^2 + π*r*sqrt(r^2 + h^2)

r is the radius at the opening and h is the cone’s vertical height (as opposed to being the slant height).

I need to find surface area for a cone… and I need the formula.

Thanks!
(Please hurry and answer, I need my good sleep and need to hit the hay soon!)

π*r^2 + π*r*sqrt(r^2 + h^2)

r is the radius at the opening and h is the cone’s vertical height (as opposed to being the slant height).