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Formulas for calculating the areas and perimeters of various two-dimensional shapes, including squares, rectangles, parallelograms, trapezoids, and triangles. Additionally, it includes formulas for the volumes and surface areas of three-dimensional figures such as rectangular figures, solids (cubes), right circular figures (cylinders, spheres, and cones), and frustums of right circular cones.
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Areas and Perimeters
Figure Sketch Area Perimeter
Square A = s
2
P = 4 s
Rectangle A = lw P = 2 l + 2 w
Parallelogram A = lh P = 2 l + 2 w
Trapezoid A = ( )
1 2
hb b P =
1 2 1 2
s s b b
Triangle A = bh
P = s s b
1 2
Area and Circumference of a Circle
Circle A =
2
r C = 2 r or C = d
l
w
l
s
h
b 1
b
2
h
s 2
s
1
s
1
s
2
h
b
r
d
w
Volumes and Surface Areas of Three- Dimensional Figures
Figure Sketch Volume Surface Area (S)
Rectangular V = lwh S = 2 lh + 2 wh + 2 wl
Solid
Cube V = s
3
S = 6 s
2
Right
Circular V = r h
2
2
2 rh 2 r
Cylinder
Sphere V =
3
r
2
4 r
Right
Circular V = r h
2
2 2
r r h
Cone
Square or
Rectangular V = lwh
Pyramid
Frustum of
Right Circular V =
2 2
r rR R h
s ( R r )
Cone
w
h l s s s h r r r
h
h
l
w
r
s
h