Circumference of a Circle: (measurement around circle)
C = pi x d (use when given diameter)
OR
3.14 x diameter *
C = pi x 2r
3.14 x 2 x radius**
The picture to the left shows a circle with a diameter of 4 yd.
*diameter goes from one side of the circle to the other through the center. You will substitute or replace the
measurement of the given diameter in for d. For example, d = 4 in; C = 3.14 x 4 or 12.56 in
*radius goes from center of circle to one side of the circle. It is half of the diameter. (r = d/2) You will substitute the
measurement of the given radius in for r.
For example, r = 3 in; C = 3.14 x 3 in or 9.42 in
Area of a Circle: (you are measuring the “area” or “space”
inside the circle.
𝐴 = 𝜋𝑟 2
A = 3.14 x radius squared
For example: Given a radius of 2 in.; A = 3.14 x 2 in x 2 in or
12.56 in squared.
Area of a semi-circle or half of a circle is: 𝐴 = 𝜋𝑟 2 / 2
For example: Given a radius of 2 in.; A = 3.14 x 2 in x 2 in / 2
or 5.28 in squared.
Area of a Triangle :(you are measuring the space
inside the triangle: A = ½ bh
Volume of a Triangular Prism: V = (B)h or
2 times the area of the base times the height of
prism.
Surface Area of a Triangular Prism: (you are
measuring the sum of the areas of all the faces or
surfaces.
SA = the sum of the area of the 2 triangles and
the sum of the area of the three rectangles;
NOTE: the rectangle areas may not be the
same. Be sure to make sure you are using the
correct l and w.
Volume of a Rectangular Prism: (you are measuring the amount in cubic units that fills the rectangular prism)
Formula: V = Bh or V = ℓwh
B= l x w
Given the rectangular prism to the right, you have a length of 5 in, width of 5 in and height of 8 in.
Substitute the values for l, w, h with the given measurements and multiply.
For example, 5 in x 5 in x 8 in = 200 in cubed.
Surface Area of a Rectangular Prism:
The sum of the areas of all the surfaces, or faces, of a three-dimensional shape is the surface area. The surface area S.A. of
a rectangular prism with length ℓ, width w, and height h is the sum of the areas of its faces.
S.A. = 2ℓw + 2ℓh + 2wh
Alternatively, replace or substitute ℓ with 4, w with 3, and h with 2 in the formula for surface area.
S. A. = 𝟐𝓵𝒘 + 𝟐𝓵𝒉 + 2wh
= 2 (4  3) + 2 (4  2) + 2 (3  2)
= 24 + 16 + 12
= 52 m squared
So, the surface area of the rectangular prism is 52 square meters.