Question

what is the formula for the area of the rhombus?

a = l × b

a = \frac{1}{2} × d₁ × d₂

a = b × h

a = \frac{1}{2} × b × h

Explanation:

Step1: Analyze each formula

• \(A = l\times b\) is the formula for the area of a rectangle.
• \(A=\frac{1}{2}\times d_1\times d_2\), where \(d_1\) and \(d_2\) are the diagonals of a rhombus. A rhombus can be divided into two congruent triangles by one of its diagonals. The area of a triangle with base \(d_1\) and height \(\frac{d_2}{2}\) is \(S=\frac{1}{2}\times d_1\times\frac{d_2}{2}\). Since there are two such triangles in a rhombus, the area of the rhombus \(A = 2\times\frac{1}{2}\times d_1\times\frac{d_2}{2}=\frac{1}{2}\times d_1\times d_2\).
• \(A = b\times h\) is the formula for the area of a parallelogram (a rhombus is a special parallelogram, but this is not the most - specific formula for a rhombus in the given options).
• \(A=\frac{1}{2}\times b\times h\) is the formula for the area of a triangle.

Answer:

\(A=\frac{1}{2}\times d_1\times d_2\)