Lesson 7:

Calculating Surface Area

Objective

In this lesson we will answer the following question:

How is surface area of a tract of land calculated using an engineering

drawing or map?

Reading Assignment

There is no reading assignment for this lesson.

Lecture

Introduction

In a later lesson, we will need an accurate estimate of the area of the watershed

affected by your construction site. This lesson introduces a method that can be

used to determine the area of any region which you have mapped at a known

scale. You can use this to determine the area of your property from the

engineer's drawing you made of its boundaries in Lesson 5. You can also use

this method to determine the area of watersheds drawn onto a topo map.

Transfer the Boundaries to Graph Paper

If you are finding the area of a tract of land represented by an engineer's drawing

on graph paper, you can skip this step. But if you are finding the area of a plot of

land on a topo map, you will first need to transfer the boundaries to graph paper.

To do so, first:

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You may find it helpful to tape the papers in place. This is best done when it is

bright and sunny outside so that light shines through your paper.

Next:

Now you have a copy of your boundaries drawn onto graph paper.

Determine the Scale

The next step is to determine the scale of your graph paper map. If you are using

the engineer's drawing which you made in Lesson 5, you should have written the

scale on your paper - we suggested a scale of 1 inch to 100 feet.

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If you are using a map traced from a topo map, then you can measure the scale

on the topo map. If the topo map has been enlarged, you must make sure that the

scale was enlarged with it.

In the example we will consider below, the scale is 1" = 100'.

Find the Area of a Grid Square

To find the area of a square on your graph paper, first measure the length of a

square. On our graph paper, a square is 0.25" long. To find the scaled length of

the square, we use the following equation:

Measured length of square × Scale = Scaled length of square

In the case of our example, the calculation is as follows:

Using the scaled length of a square, we can calculate the area of the square.

Area = (Scaled length)2

In the case of our example, the area of the square would be:

Area = (25 ft.)2

Area = 625 ft.2

Count the Squares

The next step is to count the squares within the boundaries on your graph paper.

I find it helpful to mark each square as I count it.

It is simple to count the whole squares within the boundaries, but the squares at

the edges have only a fraction of their area within the boundaries. For these

squares, I first mark and count the squares which have roughly half of their area

within the boundaries. Then the larger squares are marked as 3/4 squares and the

smaller squares as 1/4 squares. I have marked all of the squares on the

watershed map below.

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Next I input the number of squares of each type into the table below and

calculate the total number of squares within the boundaries.

Number of

squares

Multiplier Equivalent number of whole

squares

Whole

squares

256 × 1.00 256.00

3/4 squares 19 × 0.75 14.25

1/2 squares 14 × 0.50 7.00

1/4 squares 12 × 0.25 3.00

Total = 280.25

Calculate the Area

The surface area within the boundaries of the watershed can be calculated using

the following formula:

(Number of squares) × (Area of a grid square) = Total area

In the case of our example, the calculation is:

280.25 × 625 ft.2 = 175,156 ft.2

So the total area within the boundaries is 175,158 ft.2

If you wish to know the area in acres, you can use the following equation:

In the case of our example, the acreage is:

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The total acreage of the watershed on our map is 4 acres. This value can be used

in any of the calculations requiring drainage area.

Review

To determine the surface area of a mapped tract of land, use the following steps:

Transfer the boundaries onto a piece of graph paper.1.

Determine the scale of the map.2.

Determine the area of one grid square on the graph paper.3.

Count the number of grid squares within the boundaries.4.

Calculate the tract's surface area.5.

This procedure can be used to determine the area of a property from an

engineer's drawing or to find the area of a watershed on a topo map.

New Formulas Used

To determine the scaled length of a square on the graph paper:

Measured length of square × Scale = Scaled length of square

To determine the area of a square on the graph paper:

Area = (Scaled length)2

To determine the area of your tract of land:

(Number of squares) × (Area of a grid square) = Total area

To change the drainage area from square feet to acres:

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Assignment

Use the method outlined in this lesson to determine the surface area of

property you plan to build on, using the engineer's drawing you made in

Lesson 5. Does your calculated acreage match the actual acreage?

1.

Now calculate the surface area of the watershed affected by your

construction site (from Lesson 6).

2.

Finally, calculate the surface area of your construction site (from Lesson

6).

3.

Quiz

There is no quiz for this lesson.

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