A rhombus is a quadrilateral with four equal sides, often drawn like a tilted diamond. Its area can be found quickly if you know the lengths of its two diagonals. The formula Area = 1/2 x d1 x d2 matters because it works even when the height is not easy to see.
The same diagonal formula also works for a kite when the diagonals are measured across the shape.
Key Facts
- Area of a rhombus from diagonals: A = 1/2 x d1 x d2.
- The diagonals of a rhombus are perpendicular, so they meet at a 90 degree angle.
- In a rhombus, each diagonal cuts the other diagonal into two equal halves.
- A rhombus can be split by its diagonals into four right triangles.
- The formula A = 1/2 x d1 x d2 also works for a kite with perpendicular diagonals.
- Always use the same units for d1 and d2, and give area in square units.
Vocabulary
- Rhombus
- A rhombus is a quadrilateral with four sides of equal length.
- Diagonal
- A diagonal is a line segment that connects two nonadjacent vertices of a polygon.
- Kite
- A kite is a quadrilateral with two pairs of adjacent equal sides.
- Perpendicular
- Perpendicular lines meet at a right angle of 90 degrees.
- Area
- Area is the amount of flat space inside a two-dimensional figure.
Common Mistakes to Avoid
- Using A = d1 x d2 without the 1/2 factor is wrong because the diagonal rectangle contains twice the area of the rhombus or kite.
- Mixing units, such as using centimeters for d1 and meters for d2, is wrong because area calculations require consistent units before multiplying.
- Using side length instead of a diagonal is wrong because the formula A = 1/2 x d1 x d2 needs the two full diagonal lengths.
- Using half-diagonals as if they were full diagonals is wrong because the formula already accounts for the full lengths d1 and d2.
Practice Questions
- 1 A rhombus has diagonals d1 = 14 cm and d2 = 9 cm. Find its area.
- 2 A kite has diagonals 18 in and 11 in. Find its area in square inches.
- 3 Two rhombuses have the same longer diagonal, but one has a shorter second diagonal. Explain which rhombus has the smaller area and why.