By Ellen Murphy — Updated August 30, 2022

Understanding area is essential in everyday tasks: from tiling floors and sizing furniture to determining the coverage of a sprinkler system. Below is a clear, expert‑crafted guide that walks you through the math for circles, rectangles, parallelograms, triangles, trapezoids, and sectors.

Circle

Step 1: Measure the radius (r)

The radius is the distance from the center to the edge. For example, a circle might have a radius of 5 ft.

Step 2: Square the radius

Compute r². With r = 5 ft, r² = 25 ft².

Step 3: Multiply by π

The area A = π r². Using π ≈ 3.14159 gives A ≈ (3.14159)(25) = 78.54 ft².

Square or Rectangle

Step 1: Measure the height (h)

Suppose the height is 5 in.

Step 2: Measure the base (b)

Let the base be 12 in.

Step 3: Multiply base by height

Area A = b × h. Here, A = 12 in × 5 in = 60 in².

Parallelogram

Step 1: Find the altitude (v)

The vertical height might be 3 ft.

Step 2: Measure the base (b)

Let b = 5 ft.

Step 3: Multiply base by altitude

A = v × b = 3 ft × 5 ft = 15 ft².

Triangle

Step 1: Measure the vertical height (h)

Assume h = 2 in.

Step 2: Measure the base (b)

Let b = 3 in.

Step 3: Compute half the product

A = ½ b × h = 0.5 × 3 in × 2 in = 3 in².

Trapezoid

Step 1: Measure the vertical height (h)

For instance, h = 3.5 in.

Step 2: Measure the longer base (b)

Let b = 4 in.

Step 3: Measure the shorter base (a)

Let a = 3 in.

Step 4: Apply the trapezoid formula

A = ½ (a + b) × h = 0.5 × (3 in + 4 in) × 3.5 in = 12.25 in².

Sector

Step 1: Measure the radius (r)

Example: r = 6 in.

Step 2: Measure the central angle (θ)

θ is measured in radians. For example, θ = 1.05 rad.

Step 3: Calculate area

A = ½ r² × θ = 0.5 × (6 in)² × 1.05 = 18.9 in².

TL;DR

MathIsFun offers an online area calculator for quick checks. For composite shapes, compute each component’s area and sum them. Always include units (in, ft, yd).