7.2 Area & Perimeter

7.2 Area & Perimeter

Quick Answer: Perimeter is the total distance around a shape — add the sides. Area is the space inside a shape — measured in square units. On the NEX, geometry means applying a formula the question gives you — most often to rectangles, squares, triangles, and composite figures built from rectangles.

Scope Note: What the NEX Actually Asks

The NLN NEX Technical Manual (2024-03-21, §4.2) narrowed the geometry content. Circle-theory items — circumference, radius and diameter relationships, and angles — were removed. What remains is applying a given formula, plus measurement and scale.

So treat the circle material below as useful background, not a memorization requirement. If a circle appears in a NEX item, the formula will be supplied with the question; your job is to substitute correctly and report the right unit. Rectangles, squares, triangles, and composite figures are still the shapes worth practicing until the substitution is automatic.

Perimeter — Linear Units

Perimeter is the sum of the side lengths of a closed shape. It is a length, so its units are linear: inches, feet, meters, centimeters.

Worked example 1. A rectangular clinic room is 14 ft by 10 ft. What is the perimeter?

P = 2 × (14 + 10) = 2 × 24 = 48 ft.

Worked example 2. A triangular dressing covers a wound with sides 5 cm, 6 cm, and 7 cm. Find the perimeter.

P = 5 + 6 + 7 = 18 cm.

When side lengths have mixed units (for example, 2 ft and 18 in), convert to a single unit before adding.

Area — Square Units

Area measures the surface inside a shape. Because it counts squares, the units are always square: in², ft², cm², m². A common NEX trap is reporting area with a linear unit.

Worked example 3. A hospital blanket is 60 in long and 36 in wide. What is its area?

A = 60 × 36 = 2,160 in².

Worked example 4. A triangular bandage has base 12 cm and height 5 cm. Find the area.

A = ½ × 12 × 5 = ½ × 60 = 30 cm². The height here is the perpendicular height, not a slanted side.

Worked example 5. A circular wound has diameter 6 cm. Find the area.

Radius r = 6 ÷ 2 = 3 cm. A = π × r² = 3.14 × 3² = 3.14 × 9 = 28.26 cm².

Circumference — Background Only

Circumference items were removed from the NEX (Technical Manual §4.2), so this is here for completeness and for other nursing entrance tests, not as something to memorize for the NEX. Circumference is the perimeter of a circle:

• C = π × d, or
• C = 2 × π × r

Worked example 6. A circular handrail has radius 7 m. Find the circumference (use π ≈ 3.14).

C = 2 × 3.14 × 7 = 43.96 m.

Composite Figures

A composite figure is made of two or more basic shapes. Break it into rectangles (and sometimes triangles), find each area, then add (or subtract for cut-outs).

Worked example 7. An L-shaped exam room can be split into two rectangles: 8 ft × 6 ft and 4 ft × 4 ft. Find the total floor area.

Rectangle 1: 8 × 6 = 48 ft². Rectangle 2: 4 × 4 = 16 ft². Total = 48 + 16 = 64 ft².

Worked example 8. A rectangular floor 10 m by 7 m has a circular utility cut-out of radius 1 m. What is the usable floor area?

Floor area = 10 × 7 = 70 m². Cut-out = π × 1² = 3.14 m². Usable = 70 − 3.14 = 66.86 m².

Mixed Units — Convert First

Always check unit consistency before substituting into a formula.

Worked example 9. A rectangle is 1.2 m by 80 cm. Find the area in cm².

Convert 1.2 m = 120 cm. A = 120 × 80 = 9,600 cm².

If the question wants the answer in m² instead: 1.2 m × 0.8 m = 0.96 m². Same rectangle, different unit — both are correct.

Nursing-Relevant Examples

• Wound/dressing area — size a gauze pad to cover a rectangular wound 3 cm × 4 cm: area = 12 cm².
• Floor area for equipment — check whether a 2 ft × 3 ft crash cart fits in a 6 ft × 8 ft alcove: alcove area = 48 ft², cart footprint = 6 ft², so it fits.
• Circular basin — estimate the surface area of a basin with radius 5 in: A = 3.14 × 25 = 78.5 in².

Common Traps

• Using diameter as radius. Circle area uses r, not d. If you are given the diameter, halve it first.
• Forgetting the ½ in triangle area. A = ½ × b × h, not b × h.
• Area vs. perimeter units. Perimeter uses linear units (cm, m, in); area uses square units (cm², m², in²). A number followed by a linear unit when the question asked for area is a red flag.
• Using slant height for triangle area. The height in ½ × b × h is perpendicular to the base, not a side length unless the triangle is right-angled.
• Mixing units without converting. A rectangle 1.5 m × 60 cm is not 1.5 × 60 = 90. Convert one side first.