Question

The length of the diagonals of a rhombus of a rhombus are 8 cm and 14 cm. The area of one
of the 4 triangles formed by the diagonals is

(a) 12 cm² (b) 8 cm² (c) 16 cm² (d) 14 cm²

Answer 1

Let d₁ = 8 cm and d₂ = 14 cm.
Area of parallelogram = $\frac{\text{1}}{\text{2}}\left(d_1\times d_2\right)$
$$\begin{gathered} =\frac{\text{1}}{\text{2}}\left(8\times 14\right) \\ =56{\mathrm{cm}}^2 \end{gathered}$$
Since, the diagonals of a rhombus divides it into 4 equal parts, so
Area of the required triangle = $\frac{56}{4}=14{\mathrm{cm}}^2$
Hence, the correct option is (d).