Area of Kites Examples

A kite has a diagonal of 3 inches and area of 12 in². What is the length of the remaining diagonal?

This time, instead of solving for area, we can use the area formula for a kite to solve for the missing diagonal. Whether we solve for d₁ or d₂ doesn't really matter since we'll have to plug 3 inches in for the other anyway.

12 = 1.5d₂
d₂ = 8 inches

The kite has diagonals of 3 inches and 8 inches.

What is the area of the following kite?

To find the area, we need the length of both diagonals. For now, we know that one of the diagonals is 17 feet long, but the other diagonal is unknown. If we look at the individual triangles the make up the kite, we can see that we have a leg (10 ft) and a hypotenuse (13 ft). That's enough to solve for the remaining leg.

a² + b² = c²
10² + b² = 13²
100 + b² = 169

The leg we've found is only half of the missing diagonal. The diagonal is  ft, or about 16.6 ft. Now that we have the lengths of both diagonals, we can find the area.

A ≈ 141.1 ft²

A kite has a side length of 7 m and a perimeter of 20 m. If the shorter diagonal has a length of 4 m, what is the area of the kite?

We know that kites have two pairs of congruent sides. If one side is 7 m long, then we have another side of the same length. The remaining 6 m of perimeter is split up evenly too, so we have two sides of length 7 m and two sides of length 3 m.

We know that the shorter diagonal is 4 m long, which means we can find the length of the other diagonal using the Pythagorean Theorem for each portion of the unknown diagonal. The first triangle has a leg of 2 m and a hypotenuse of 3 m.

a² + b² = c²
2² + b² = 3²
b² = 5

The other triangle has a leg of 2 m and a hypotenuse of 7 m.

a² + b² = c²
2² + b² = 7²
b² = 45

If we combine them, we can see that the unknown diagonal has a length of . Calculating the area shouldn't be a problem now.

A = 17.9 m²