Geometry » Calculating area of compound figures

Calculating the area of a compound figure works as follows:

1. Divide the figure into known figures like rectangle and (semi-)circles.
2. Calculate the area of the separate figures.
3. Calculate the area of the whole figure by adding the area of the separate figures.

Example

Calculate the area of the following figure in m2.
octagon ABCDEFGH, at every vertex the figure makes an angle of 90°, at A to the right, at B to the left, at C to the right, at D to the right, at E to the left, at F to the left, at G to the left, at H to the left to join point A at the end of line AH.

Divide the figure into separate figures. In this case three rectangles.

same octagon with lines BC extended (to T on line GH) and DE extended (to S on line GH). Known is AB=120, BC=65, CD=110, EF=85, GF=115 and AH=135

To calculate all the areas, we need the length of CT (or DS).
CT = DS = 135 – 65 = 70 cm

Now we can calculate the areas.
Area rectangle left = 120 × 135 = 16200 cm 2
Area rectangle middle = 110 × 70 = 7700 cm2
Area rectangle right = 85 × 115 = 9775 cm2

Area whole figure = 16200 + 7700 + 9775 = 33675 cm2 = 3,3675 m2


Other method

The figure can also be divided into other rectangles.
Below, you can see one of these ways.
sSame octagon with CD extended in both directions. The line towards the left intersects line AH in point T and the line towards the right intersects line FG in point S
However, this method gives us more unknown sides that we need. We now need HT (or GS), GH (or ST) and DE (or FS) before we can calculate the areas.
HT = GS = 135 – 65 = 70 cm
GH = ST = 120 + 110 + 85 = 315 cm
DE = FS = 65 - (135 - 115) = 45 cm

Now we can calculate the areas.
Area rectangle ABCT = 120 × 65 = 7800 cm 2
Area rectangle TSGH = 315 × 70 = 22050 cm2
Area rectangle EFSD = 85 × 45 = 3825 cm2

Area whole figure = 7800 + 22050 + 3825 = 33675 cm2 = 3,3675 m2