Perimeter of a Kite Formula 2(a+b) with Examples

Key Points

• The perimeter of a kite formula is $P = 2(a+b)$, where $a$ and $b$ are the lengths of the two distinct pairs of sides.

• A kite has two pairs of adjacent equal sides, so only two different side lengths exist however irregular it looks.

• Diagonals never appear in the perimeter, because the perimeter runs around the boundary and diagonals cut across the interior.

• When $a = b$ the kite becomes a rhombus and the formula collapses to $P = 4a$.

• Finding a missing side from the perimeter means halving first, since $\frac{P}{2} = a+b$.

What Is the Perimeter of a Kite Formula?

The perimeter of a kite formula adds the four boundary sides, which reduce to two distinct lengths:

$$P = a + a + b + b = 2(a+b)$$

A kite is a quadrilateral with two pairs of adjacent equal sides. Those pairs are what make the four-term sum collapse into a doubled bracket.

Why Only Two Lengths Are Needed

A general quadrilateral needs all four sides adding, because all four can differ. A kite is more constrained: its defining property is that the equal sides come in adjacent pairs.

So if one pair measures $a$ and the other measures $b$, the full boundary is $a + a + b + b$. Factoring gives $2(a+b)$, which is why two measurements are enough.

The adjacency matters. A parallelogram also has two pairs of equal sides, but its equal sides are opposite rather than adjacent, and it happens to share the same perimeter formula for a different structural reason.

Variable Key

Examples of the Perimeter of a Kite Formula

Example 1

A kite has side pairs of 6 cm and 10 cm. Find its perimeter.

$$P = 2(6+10) = 2(16) = 32$$

Final answer: 32 cm

Example 2

A kite has sides 8 cm and 15 cm and diagonals 12 cm and 20 cm. Find its perimeter.

Four numbers are given, so adding them all looks like the way to a perimeter:

$$8 + 15 + 12 + 20 = 55$$

That mixes two different kinds of length. A perimeter is the distance round the outside, and the diagonals run through the interior from corner to corner, so they are not part of the boundary at all.

Only the sides count, each pair twice:

$$P = 2(8+15) = 2(23) = 46$$

Final answer: 46 cm. The diagonals belong to the area formula, $\frac{1}{2}d_1 d_2 = 120$ square cm, not to the perimeter.

Example 3

A kite has perimeter 54 m and one pair of sides measuring 11 m. Find the other pair.

Halve the perimeter first, because $\frac{P}{2} = a+b$:

$$a + b = 27, \qquad b = 27 - 11 = 16$$

Final answer: 16 m

Example 4

A kite has all four sides equal to 9 inches. Find its perimeter and name the shape.

$$P = 2(9+9) = 36$$

Final answer: 36 inches, and with all four sides equal the kite is a rhombus.

A rhombus is a special kite, so the general formula still applies and simply reduces to $4a$.

Example 5

A kite-shaped garden bed has sides of 2.5 m and 4.2 m. How much edging is needed, and what if 10 per cent extra is allowed for cuts?

$$P = 2(2.5+4.2) = 2(6.7) = 13.4$$ $$13.4 \times 1.10 = 14.74$$

Final answer: 13.4 m of edging, or 14.74 m with the 10 per cent allowance.

Don't Confuse These Four Quadrilateral Perimeters

Kite and parallelogram share a formula but not a reason. In a kite the equal sides touch at a vertex; in a parallelogram they face each other across the shape.

Perimeter of a Kite, Where Things Go Sideways

Mistake 1: Including the diagonals

Where it slips in: Kite questions usually supply the diagonals too, because the area formula needs them, so all four figures look like inputs.

Don't do this: $P = a + b + d_1 + d_2$

The correct way: $P = 2(a+b)$. Diagonals are interior segments and belong to the area calculation.

Students who trace the outline with a finger before writing anything down never include a diagonal, because the finger simply does not travel along one. Asking what a perimeter physically is settles which measurements qualify.

Mistake 2: Treating all four sides as different

Where it slips in: A kite looks asymmetric, so four separate side lengths seem plausible.

Don't do this: Look for four distinct side measurements.

The correct way: A kite has exactly two distinct side lengths by definition. If a question appears to give four different sides, the shape is a general quadrilateral, not a kite.

Mistake 3: Forgetting to halve when working backwards

Where it slips in: The perimeter is given and one side is wanted, so the known side is subtracted from the perimeter directly.

Don't do this: $b = P - a$

The correct way: $b = \frac{P}{2} - a$. Since $P = 2(a+b)$, the halving comes first, and skipping it roughly doubles the answer.

Wrapping Up

• The perimeter of a kite formula is $P = 2(a+b)$, using the two distinct side lengths.

• Only the boundary counts, so diagonals belong to the area formula and never to the perimeter.

• A kite has exactly two distinct side lengths, however irregular the shape appears.

• Working backwards from a perimeter means halving before subtracting.

• To work through quadrilateral geometry with a teacher, explore a geometry tutor or math tutoring.

Five Minutes of Practice

Find the perimeter of a kite with sides 7 cm and 13 cm. Then find the missing side of a kite whose perimeter is 68 m and whose other pair measures 14 m.

Want a live Bhanzu trainer to walk through more geometry problems? Book a free demo class.

Read More

• Difference Between Kite and Rhombus

• Perimeter Formula

• Angles of a Quadrilateral

• Area vs Perimeter

• Cyclic Quadrilaterals