Question

what is the formula for the area of a kite? lw 1/2d₁d₂ bh 1/2bh rewatch

Explanation:

A kite is a quadrilateral with two distinct pairs of adjacent sides that are equal in length. The formula for the area of a kite is derived from the fact that a kite can be divided into two congruent triangles. If the lengths of the diagonals of the kite are \(d_1\) and \(d_2\), then the area \(A\) of the kite is the sum of the areas of these two triangles. The area of a triangle is \(\frac{1}{2}\times base\times height\). For each triangle in the kite, if we consider one diagonal as the base and half of the other diagonal as the height, then the area of each triangle is \(\frac{1}{2}\times\frac{d_1}{2}\times d_2\) (assuming \(d_1\) and \(d_2\) are the diagonals). Since there are two such triangles, the total area \(A = 2\times\frac{1}{2}\times\frac{d_1}{2}\times d_2=\frac{1}{2}d_1d_2\).

• \(lw\) is the formula for the area of a rectangle (where \(l\) is length and \(w\) is width).
• \(bh\) is the formula for the area of a parallelogram (where \(b\) is base and \(h\) is height).
• \(\frac{1}{2}bh\) is the formula for the area of a triangle (where \(b\) is base and \(h\) is height).

Answer:

\(\frac{1}{2}d_1d_2\) (i.e., the option \(1/2d_1d_2\))