Search
Calculating Area of Rectangles
. . . . . . .
. . . . . . . . .
1. Our Training Videos
Skills Application: Calculating Area of Rectangles
Step-by-Step: Calculating Area of Rectangles
. . . . . . . . .
2. Running with Pi

## Tagged in

Realtors assess/verify the total area of homes prior to listing them for sale. They measure all the rooms, decks, garages, calculate their areas and calculate the total area of the home. Accuracy in area calculations is important for listing a home for sale, legal documents are also based on these area calculations.

## Running with Pi

. . . . . . . . .
3. Our Training Worksheets

In this lesson you will learn about some 3-dimensional simple shapes and know how to calculate their surface area.

Rectangular prism

The first shape is rectangular prism or cube. The best example of cube is a box. Another example is a room. Surface area of a room is useful for painting the room.

Each cube has three dimensions; width, length and height, say W, L and H. Surface area of a cube consists of six rectangles or three pairs of rectangles. In each pair there are two identical rectangles. One pair with dimensions W and L. The second pair with dimensions W and H and the last pair with dimensions L and H.

Rectangular Prism

Surface area of a rectangular prism or cube is:

A = 2 (WL+WH+LH)

Example:

Surface area of a rectangular prism with dimensions 2, 3 and 5 meters is:

A = 2 (2×3 + 2×5 + 3×5) = 42 m2

Cylinder

The surface area of a cylinder consists of surfaces of 2 circles and one rectangle. See the following figure.

Cylinder

The surface area of a cylinder with radius r and height h is:

A = 2πr2 + 2π rh

Example:

Find surface area of a cylinder with radius 4 and height 6 inches.

A = 2πr2 + 2π rh = 2π (4)2 + 2π×4 × 6 ≈ 251.2 in2

### A Short Review

Area of a rectangle is calculated by multiplying its Length by its Width:

A = L · W

Depending on where a rectangle is, Length and Width may be replaced by 2 other measurements. The Area to be laminated on the edge of a counter top is better described by the words Thickness and Depth. (See the Advanced tab for more examples and explanation)

A = Th · D

Regardless of the words used, the math stays the same: multiply 2 numbers to get a third.

Rectangles are often found as parts of complex shapes: a box is made of 6 rectangles, a cylinder is made of 2 circles and 1 rectangle, all prisms have a number of rectangles that make up the sides. Look for rectangles in objects.

### Worksheet: Level 1

The operations used are clearly specified. Only one type of mathematical operation is used in a task.

### Worksheet: Level 1 Sample Questions

Example:

Further Examples:

Doors dont have a Length. What measurement words describe a doors dimensions that can be used for calculating the Area of its:

1. front?
2. side edges?
3. top & bottom edges?

### Worksheet: Level 2

Tasks involve one or two types of mathematical operation. Few steps of calculation are required.

### Worksheet: Level 2 Sample Questions

Calculate the area of the following rectangles, answer in decimals.

Example:

What is the area of a rectangle with a length of 150 yd and a width of 65 yd?

L × w = A

length × width = area

150 × 65 = 9750 yd2

Question:

1. w = 4, L = 5

Further Example:

Calculate the Area of a 3 ½ inch x 15 ¾ inch rectangle. Name the resultant unit of measure.

### Worksheet: Level 2 Sample Answer Key

L × w = A

length × width = area

5 × 4 = 20

### Worksheet: Level 3

Tasks require a combination of operations. Several steps of calculation are required.

### Worksheet: Level 3 Sample Questions

Calculate the following. Answer in decimals:

Example:

What is the area of a Canadian football ﬁeld with a length of 150 yd and a width of 65 yd?

L × w = A

length × width = area

150 × 65 = 9750 yd²

Question:

1. What is the area of a sheet of glass, w = 4 ft, L = 7 ft?

Further Example:

Whats the surface Area of a letter-size sheet of paper? Answer in [in²].

### Worksheet: Level 3 Sample Answer Key

L × w = A

length × width = area

4 ft × 7 ft = 27 ft²

Tasks involve multiple steps of calculation. Advanced mathematical techniques may be required.

### Additional Information: Measurement math connections for trades & technology.

Measurement math connections for trades & technology.

Calculating the Area of Rectangles involves working with Length and Width.

Length or Distance is a 1-D or 1 dimensional concept. It means it runs in 1 direction or in a single line. For this reason it is called linear. It can be measured directly with rulers, tape measures, reflected laser beams in distance finders.

There are many synonyms or alternative names for Length. Some of these names include radius, caliber, depth, or edge. (See table below) These are all linear concepts. Any 2 of these can combine to indicate Area. For example Depth and Length of a trench can combine to express the Sidewall Area of a trench to be shored against collapsing, or Width and Thickness can combine to express the Cross-Sectional Area of metal in a spoons handle.

Area is a 2-D or 2 dimensional concept. It can relate to shapes (2-D things) and objects (3-D things). It spreads in 2 linear directions or in a surface plain. For this reason it is called planar. It can not directly be measured since measurement tools are linear. Planar (area) “measurements” are always calculated from linear measurements. Some digital instruments say they “measure” Area, but it cannot be measured directly. These instruments calculate area from reflected laser beam Distance measurements.

Area surfaces can be very irregular or very smooth and regular. Area coverage can be partial or full.

### Additional Information: Sample Definitions & Conversion Data Table

 Property of matter being measured: possible synonyms symbol Unit of measure Metric symbol Imperial & US symbol Distance (1-D) in straight line: straight lines of circles: loops (full or part) & : length, width, height, depth, thickness, gauge, side, edge, strain L or l, w, h, d, th, ga. s, e, e (greek epsilon) meter and other prefixes (kilo, centi, …) m mile, fathom mi, fm diameter, caliber, bore radius, chord d or Ø, cal, b or Ø,  r, ch furlong, yard fur, yd, perimeter, circumference, arc, stroke p or P, c, a, s feet, inch, barleycorn, point ft, in - pt Area (2-D) surface area, coverage, wrap A meter squared and other prefixes (kilo, centi, …) hectar mi², ha square mile, square yard, square feet, square inch mi², yd², ft²,in² inch, acre ac circular mils, square mils CMs, SMs

### Additional Information: Another Way to Get the Answer

Another Way to Get the Answer

Calculate the side area of a boiler (cylinder) if the diameter is 0.5 m, circumference is 1.57 m and height is 1.25 m

Layout your calculations neatly, so you can review, track changes, correct or learn from them. One way a layout can look is like this: