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Basic Geometry

Basic Geometry

Example 1

3 x 3 x 3 cube

This cube has six congruent faces, each with a length and width of 3 cm.

Area of one face = 3 x 3 cm = 9 cm2

Surface area = 6 sides x 9 cm2 = 54 cm2

Example 2

Trapezoidal prism

This trapezoidal prism has six sides, two congruent trapezoids and four rectangles.

Trap 1½(10 + 4) x 214 cm2
Trap 2½(10 + 4) x 214 cm2
Rect 13.6 x 7.025.2 cm2
Rect 24.0 x 7.028 cm2
Rect 33.6 x 7.025.2 cm2
Rect 410.0 x 7.070 cm2
Total176.4 cm2

Example 3

4 x 5.8 cylinder

This cylinder has two circles (each with a radius of 2 cm) and one rectangle (with a length of 5.8 cm and a width the circumference of the circles).

Circle 1π x 22   
= 4π
12.56 cm2
Circle 2π x 22   
= 4π
12.56 cm2
Rect 15.8 x 4π
= 23.2π
72.85 cm2
Total97.97 cm2

Example 4

This pyramid is made up of four equilateral triangles.

6.9 x 8.0 Triangle

Here we just need to find the area of one triangle and multiply it by four sides:

Area of 1 triangle = ½bh = ½(8 x 6.9) = 27.6 cm2

Now, multiply that by four sides, and we're done.

110.4 cm2

Example 5

Sphere

The diameter of this sphere is 11.9 cm, so the radius is half of that, 5.95 cm.

Surface Area = 4(pi)(5.95)^2 = 141.61 (pi) cm^2 = 444.66 cm^2

Example 6

Cone

The area of the circular base is equal to:

(pi)(5^2) = 25 (pi) cm^2 = 78.5 cm^2

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