Calculate Deltoid Area: Shape with Diagonals 6cm and 10cm

A deltoid (or kite) is a quadrilateral with two pairs of adjacent equal sides. In this problem, AD = AB and CA = CB. Unlike rectangles or parallelograms, deltoids have perpendicular diagonals that intersect at right angles.

Diagonals are lines that connect opposite vertices and cross through the interior of the shape. In deltoid ACBD, the diagonals are AC (length 6) and BD (length 10). Side lengths like AB are the edges of the shape.

The diagonals divide the deltoid into four triangles. The formula $\frac{d_1 \times d_2}{2}$ calculates the total area by finding the area of the rectangle formed by the diagonals, then dividing by 2 since the deltoid occupies half that space.

No! This formula $\frac{d_1 \times d_2}{2}$ only works for shapes with perpendicular diagonals, like deltoids, rhombuses, and squares. For other quadrilaterals, you need different formulas.

If diagonals aren't perpendicular, you'd need a more complex formula involving the sine of the angle between them: $\frac{d_1 \times d_2 \times \sin(\theta)}{2}$. But deltoids always have perpendicular diagonals, so we use the simpler version!