Area can be calculated by breaking up a composite shape into simple shapes and adding up their areas. Watch the video to see calculating the area of a feature wall.
Parallelograms, Trapezoids, Hexagons, Octagons and other geometric shapes can be broken up into triangles and rectangles. Their areas can also be calculated by adding up the areas of those triangles and rectangles. See Episodes 19 & 21 on area of rectangles and triangles.
Sometimes the above lengthy approach can be shortened. You can find formulas below that condense the area calculations into 1 short formula.
A parallelogram is a skewed rectangle. Base (B) is measured along its long side, height (h) is measured inside or outside the shape perpendicularly to the base.
A = B ∙ h
The area (A) of a parallelogram with a base B = 5 cm, and a height h = 4 cm is
A = 5 x 4 = 20 cm2
A trapezoid has a shorter base (b) and a longer base (B) and a height (h) that is measured inside or outside the shape perpendicularly to the base.
The area (A) of a trapezoid with a long base B = 6 cm, a short base b = 4 cm and a height h = 3 cm is
A hexagon is any six-sided closed figure. The hexagons used most often in building construction are regular hexagons.
Area of a Regular Hexagon with side "a":
The area of a hexagon with side = 4 centimeters is
An octagon is any eight-sided closed figure. The octagons used most often in building construction are regular octagons. A simple example of a regular octagon is STOP sign. The area of a regular octagon can be found by breaking it into eight identical isosceles triangles; however, we will use one of the following shortcut formula.
Area of a Regular Octagon with side “a”:
The area of an octagon with side 2 inches is:
Check out the ADVANCED tab. The exercise will further your understanding and help with building a bigger mental picture. It builds links between numbers and algebra. Take your time and make the comparisons. It is important to cross-link the concepts of area and numbers.