### Surface Area

The surface area of a figure, is the total area of all the sides of the figure.

Triangular Prism(Right Angle Triangle)

To find the surface area of the prism above, follow the steps below.

Step 1: Divide the figure into smaller shapes.

Step 2: Find the area of each smaller shape.

Step 3: Add the areas of each smaller shape.

A right-angle triangle prisim can be divided into five smaller shapes; two right angle triangles and three rectangles.

Example

Find the surface area of the prism below.

Pyramid

A pyramid is an object which has: a straight sided shape base (a squared, rectangular, trianglular base etc) and triangular sides which meet at the top (called the apex).

Example

Cylinder

To find the surface area of the cylinder above, follow the steps below.

Step 1: Divide the figure into smaller shapes.

Step 2: Find the area of each smaller shape.

Step 3: Add the areas of each smaller shape.

A cylinder can be divided into three segements: two circles and a curved surface area.

The area of a circle, A = πr^{2}

Since there are two circles in a cylinder, multiply the abover formula by 2, that is:

The area of the circles, A = 2πr^{2}

The curved surface area, C.S.A. = 2πrh

The area of a cylinder, A = Area of the circles + C.S.A.

= 2πr^{2} + 2πrh

= 2πr (r + h)

Example

Cube

A cube has 6 sides (faces) of the same surface area. Each side (face) of the cube are squares. Recall, the area of a square, A = L^{2 }.

The surface area of a cube, A = 6L^{2}

Where, L is the length of a side of the cube(all the sides of a cube are the same length).

Example

Cuboid

The surface area of a cuboid, A = 2Lw + 2 Lh + 2wh

Where, L is the length of the cuboid

w is the width of the cuboid

And, h is the height of the cuboid.

Example

Sphere

A sphere is a three-dimensional object (such as a ball or the earth) with every point on the surface equidistant (halfway from) from the center.

The surface area of a sphere, A = 4πr^{2}

Where, r is the radius of the sphere.

Example

Surface Area of a sphere, A = 4 πr^{2}