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# How to calculate the area of an irregular surface

Updated February 21, 2017

You can estimate the area of an irregular surface by using the offset rule, in which you divide the shape into rectangle-shaped sections and add up the area of the rectangles. The more divisions you make, the more accurately you can estimate the area. An more accurate (but also more complicated) method for estimating the area is to divide it into shapes whose area you can calculate, such as right triangles, circles and rectangles

Find and draw the "length line," the longest line between two edges of your surface. Measure the length of this line.

Draw parallel, equally spaced "offset lines" going through the surface at right angles to your length line. If the length line measured 12 metres (40 feet), you could divide it into four sections measuring 3 metres (10 feet) wide by drawing three offset lines, or eight sections measuring 1.5 metre (5 feet) wide by drawing seven offset lines. The more offset lines you draw, the closer your estimated area will be to the true area. Five or more offset lines will usually result in a close approximation.

Measure each of the offset lines from edge to edge (with the same units you used to measure the length line) and add up their lengths. Multiply this number by the measure of the length line to get the approximate area of the surface.

Measure the distance between offset lines (it should be equal to the length of the length line divided by the number of sections). Multiply this number by the answer from Step 3 to get the approximate area of the surface.

Draw lines from one edge to another of the irregular shape until you have divided he shape into a combination of rectangles, right triangles and circles or semicircles. It's all right if the shapes do not fit perfectly into the irregular surface. Gaps left over in the surface will cause a slight under-approximation of the area. Shapes spilling over the boundary will cause a slight over-approximation.

Calculate the area of each shape using the area formulas for triangles, rectangles and circles. The area of a right triangle is equal to half of the product of the two legs (sides that make up the right angle). The area of a rectangle is equal to the base times the height. The area of a circle is equal to pi (3.14) times the square of the radius (distance from the centre of the circle to the edge).

Add up the areas of the shapes to get an approximation of the area of the irregular surface.

#### Things You'll Need

• Map or drawing of surface
• Ruler