Write a single formula for area that will work for a rectangle, a parallelogram, a trapezoid, a triangle, and a square. Explain how it works.

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Find one single formula that will work for finding the area of the following shapes: a rectangle, a square, a triangle, a parallelogram, and a trapezoid.

KEY:

A is the top side
B is the base side
H is the vertical height.

ANSWER:

A= 1/2h (a+b)

This is how we worked it out.

We didn't know the formula for the area of a trapezoid so we worked that out first. That came out to be 1/2h (a+b). We then took the basic formulas of the other shapes and tried to change them to match the trapezoid formula. This took a long time. Eventually, we worked out that every shape can have the formula 1/2h (a+b).

Trapezoid

The formula 1/2h (a+b) comes from the trapezoid. To get this we first cut off the two triangles and placed them together. We used LxW to get the rectangle formula and 1/2 bh to get the triangles' area. We later figured out 1/2h (a+b) was a quicker and more efficient way for finding area.

Rectangle

1/2h (a+b) works for a rectangle if you halve the height and multiply it by the top and the bottom added together. You get the same answer using the basic formula LxW.

Square

1/2h (a+b) works but a, h, h all equal the same so a, b, or h squared are much simpler options. 1/2h (a+b) or 1/2 6 (6+6) = 36, whereas LxW or 6x6 = 36. Both formulas get the same answers.

Triangle

1/2 bh=
1/2 hb=
1/2h (0+b)=
1/2h (a+b)

Parallelogram

We took off the right angle triangle on the left hand side of the parallelogram where 'a' finishes. We placed it on the right hand side to form a rectangle. We then used the rectangle formula to find the area.