Area Formulae

Area of a Rectangle:

What is the formula for the area of a rectangle?

"A rectangular garden bed is 8 meters long and 3 meters wide. What is the total area of the grass?"

Logic: You are multiplying the two perpendicular sides to find how many squares fit inside.

Formula:

A = lw

Where: l = length, w = width, A = Area.

Area of a Square: How do I calculate the area of a square?

"Find the area of a square tile with a side length of 15cm."

Logic: Since all sides are equal, you are just multiplying the side by itself.

Formula:

A = s²

Where: s = length of one side, A = Area.

Area of a Triangle: What is the formula for the area of a triangle?

"A triangle has a base of 10cm and a vertical height of 6cm. Find its area."

Logic: A triangle is exactly half of a rectangle with the same base and height.

Formula: Area = ½bh

Where: b = base, h = vertical height (not the slanted side), A = Area.

Area of a Circle: How do I find the area of a circle?

"A circular rug has a radius of 2 meters. What is the area of the floor it covers?"

Logic: This tells you how much space is inside the curved boundary.

Formula: A = πr².

Where: r = radius, A = Area.

Area of a Parallelogram:

What is the formula for the area of a parallelogram?

"Find the area of a parallelogram with a base of 12cm and a vertical height of 7cm."

Logic: If you cut the "triangle" off one end and moved it to the other, it would be a rectangle.

Formula: A = bh.

Where: b = base, h = vertical height, A = Area.

Area of a Trapezium: How do I calculate the area of a trapezium?

"A trapezium has parallel sides of 8cm and 10cm, and the distance between them is 5cm. Find the area."

Logic: You are taking the average of the two parallel "bases" and multiplying by the height.

Formula: A = h(½(a+b))

Where: a and b are the parallel sides, h = vertical height, A = Area.

Area of a Rhombus or Kite: What is the formula for the area of a rhombus or kite?

"A kite has diagonals measuring 10cm and 6cm. What is its area?"

Logic: You multiply the two diagonal lines (corner to opposite corner) and halve the result.

Formula: A = ½xy.

Where: x and y are the lengths of the diagonals, A = Area.

Area of a Sector (Slice of a Circle): How do I find the area of a "pizza slice" sector?

"Find the area of a sector with a 60-degree angle and a radius of 9cm."

Logic: You find the area of the full circle first, then multiply by the fraction of the circle you actually have.

Formula: A = πr²( θ/360).

Where: θ = angle = the degrees at the center, A = area, r = radius

Composite Shapes (Logic): How do I find the area of a shape made of multiple parts?

"Find the area of an L-shaped room."

Logic: Break the shape into smaller, familiar rectangles or triangles.

Find the area of each piece separately and add them together.

Formula:

A = x = A of y + A of z

Where: A = area, x = composite shape, y and z = parts of the composite shape

Shaded Region (Logic): How do I find the area of a shaded region inside another shape?

"A small circle is inside a large square. Find the area of the square that is NOT covered by the circle."

Logic: Find the area of the "outer" shape and subtract the area of the "inner" shape.

Formula: A = A of x - A of y.

Where: A = Area, x = Larger shape, y = smaller shape