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Examples for

Step-by-Step Geometry

Triangles

See the steps to compute general properties of a triangle.

Determine the perimeter of a triangle step by step:

triangle perimeter with edge lengths 5, 6, 7

Compute the area of a triangle:

area of a triangle with base 3, height 2
7, 3, 6 triangle area

Compute an isosceles triangle's area or perimeter:

isosceles triangle area with base 3 and side 4
isosceles triangle perimeter with base 6 and side 5

Compute the area of an equilateral triangle:

area of an equilateral triangle with side 7

Polygons

Explore various properties of regular polygons:

regular hexagon with side length 1
7-gon with edge length = 5

Find step-by-step solutions for determining particular properties of a regular polygon:

find the side length of a regular hexagon with apothem = 4
nonagon perimeter = 9. What is the area?
what is an 11-gon's area given side lengths of 2/3
what is edge length of a regular dodecagon with a perimeter 18

Prisms

See the steps to compute a particular dimension of a given prism:

regular triangular prism surface area 12*sqrt(3), depth 2 what is the edge length
a box has height 3 and width 2 with volume 6, what is its depth?
height of pentagonal prism with volume=6, base area = 9

Explore the relationship between a prism's surface area and edge length:

triangular prism surface area 27/2sqrt(3), depth sqrt(3) what is the edge length
find the edge length of a cube with surface area = 4
compute the surface area of a rectangular prism with width 1, depth 3 and height 6
surface area of dodecagonal prism with side length=.68, height = 3.6

Compute a prism's volume based on its side lengths:

Find the volume of a triangle prism of height 7 with base edge 4
what is a right rectangular prism's volume given side lengths 3,6,4
cuboid with side lengths sqrt(3), pi, 2sqrt(3), whats volume?
hexagonal prism with side length 1, height 6, volume = ?

Calculate areas of prisms based on their volume:

triangular prism surface area given volume is sqrt(3)/8
Lateral area of a cube with volume 9
octagonal prism with volume 36 and edge 2 what is surface area

Cones

Show how to find the height of cones:

calculate cone's height given base area is 11 and volume is 16
find the height of a cone with surface area 2pi and slant height 4
compute the height of a cone with lateral surface area = 8 and radius = 3/2

Calculate a cone's slant height:

find a cone's slant height with a base area = 9*pi, height = 16
determine the slant height of a cone with volume = 5 pi and radius = 2
cone with lateral area 3 and base 3pi, determine the slant height

Compute the lateral surface area for cones:

what is the cone lateral surface area with height = 9 and volume = 13 pi
what is the lateral surface area of a cone given surface area 10 and base area 3

Explore step-by-step solutions for determining the volume of cones:

evaluate a cone's volume given base area is 8 and height is 2
calculate the finite cone's volume given surface area is 6pi and circumference is 4

Line Equations

Determine the equation of a line:

equation of line through (2, 5), (4, 1)
equation of line with x intercept -4 and y intercept 3
line with y intercept -4 and slope 5
line with slope 2 through (1, 3)

Quadrilaterals

Explore step-by-step solutions for computing perimeters of squares:

perimeter of square with side 3
the square perimeter with a diagonal of 2 is

Calculate areas of squares:

the square's area with a diagonal 7
square area given perimeter = 12

Learn how to solve for different properties of squares:

calculate a square's diagonal with a side length of 3*sqrt 2
compute the square edge lengths with diagonal = 14
what is the square apothem given edge length of 13

See the steps to evaluate a rectangle's perimeter:

find the perimeter of a rectangle with side lengths 7/3 and 1/2
the perimeter of a rectangle with diagonal 6 and height 4 is

Compute the area of a rectangle:

rectangle area with side lengths 4 and 2
compute the area of a rectangle with diagonal 5 and height 3

Calculate side lengths of rectangles:

height of a rectangle with width 4 and area 12
what's a rectangle's base with height 4 and perimeter 17
evaluate rectangle's height with diagonal = 2, base = 1

Compute the perimeter of a parallelogram:

parallelogram perimeter side lengths 3 and 5
evaluate the perimeter of a parallelogram with edges 5 and 14 with angle pi/6

Evaluate the area of a parallelogram:

parallelogram with edges 4 and 6, with 30 degree angle, find the area
evaluate the area of a parallelogram given sides = 6 and 3

Determine the symbolic area of a rhombus step by step:

area of a rhombus with side 3

Compute a rhombus's perimeter:

rhombus perimeter, side 7

Figure out the area of a trapezoid:

trapezoid area given bases 7 and 6 and height 4

Calculate the perimeter of irregular quadrilaterals:

quadrilateral perimeter given sides 7, 6, 2 and 8

Circles

Explore general properties of circles step by step:

circle with radius 1/2

Find the area of a circle:

area of a circle with radius 2
circle with diameter 3, what is the area?
Find area when circumference is 4pi

See the steps to evaluate the circumference from different starting information:

Calculate the circumference of a circle given radius=6
Find the circumference of a circle with diameter 3
circumference of a circle with curvature 1/3
circle area = Pi/4, circumference = ?

Compute the curvature:

circle curvature when radius is 8
circle with area 4 curvature
find curvature of a circle with diameter 6
area of a circle is 25, what is the curvature?

Cylinders

Determine the radius of a cylinder:

cylinder's radius with a surface area pi^2 and height 1/2
find a cylinder's radius with a lateral surface area 6 and height 3

Solve for a cylinder's surface area:

find cylinder's surface area given radius = 1 and volume = 4 pi
evaluate a cylinder's surface area with height 3 and diameter 2
compute the surface area of a cylinder given lateral surface area = pi and base area = 1

See the step-by-step solutions for lateral surface area computations for cylinders:

determine the lateral surface area of a cylinder with a surface area 6 and radius 1/3
find cylinder's surface area given radius = 2 and volume = 4 pi
determine the cylinder lateral surface area given volume = 5 pi and radius = 2

Compute the steps to find the volume of a cylinder:

evaluate a cylinder's volume given radius is 2 and height 3/4
determine a cylinder's volume given height 3 and diameter 2
cylinder volume with surface area 8pi and height 1
cylinder's volume given lateral surface area = 6pi and radius 3

Spheres

Find the volume of a sphere step by step:

what's a sphere's volume given it's radius is 4
calculate the volume of a sphere with a surface area of 9

Follow the steps to calculate a sphere's surface area:

find the surface area of a sphere with radius = 8
determine a sphere's surface area with a diameter of 9

Find the diameter and radius from a sphere's volume:

compute the sphere diameter when the volume is 5
volume of a ball is 6, what is the radius?

Coordinate Conversions

Convert between coordinate systems step by step:

x=1/2, y=Sqrt[3]/2 to polar
r=2, t=pi/6 to Cartesian
convert r=t^2+1 to cartesian
express x^2+y^2=3 in polar coordinates

RELATED EXAMPLES

  • Coordinate Geometry
  • Geometry
  • Plane Geometry
  • Solid Geometry

    • Inscribed & Circumscribed Shapes

    Compute the areas of regular polygons inscribed in a circle:

    regular triangle with circumradius 2, what is the area
    area of square with circumradius 1/2

    Explore the relation between circumradius and perimeter:

    circumradius of an octagon with perimeter 24
    circumradius of a hexagon with perimeter 18

    Calculate the radius of a circle inscribed in a given triangle:

    compute the inradius of a triangle with sides 4, 7, and 8

    Determine the radius of a circle circumscribing a particular triangle:

    circumradius of a triangle with edges 3, 5, and 7
    equilateral triangle with side 3, find the circumradius

    Pyramids

    See the steps for computing the height of pyramids:

    what is a square pyramid's height with a base edge of 2 and volume of 7
    compute the hexagonal pyramid's height with a surface area 5 and base edge length 2/7
    find the height of a hexagonal pyramid with lateral surface area = 8 and base edge length = 1

    Find a pyramid's slant height:

    what is hexagonal pyramid's slant height with a base edge length = 1 and height = 2
    find the square pyramid slant height with lateral surface area = 1

    Learn how to determine the surface area and lateral surface area for pyramids:

    what is hexagonal pyramid's surface area given base edge length = 7/4 and slant height = 7/3
    determine a hexagonal pyramid's surface area with a base edge length 5
    a hexagonal pyramid's lateral surface area with height 9
    calculate a hexagonal pyramid's lateral surface area with a slant height 8
    find a hexagonal pyramid's lateral surface area with a volume 5 and base area 3

    Calculate a pyramid's volume step by step:

    evaluate a pentagonal pyramid's volume with a base edge length = 3, and height = 6

    Line & Point Properties

    Calculate the distance between two points step by step:

    distance between (3, 2) and (5, 1)

    Find the distance between points in 3D space:

    (2, -4, 7) to (-4, 6, 1) distance

    Find the midpoint of a line segment:

    midpoint (1, 2, 3), (2, 3, 4)
    slope of line through (2, 3) and (4, -1)
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