Question

Find the area of a rhombus, the lengths of whose diagonals are:

(i) 16 cm and 28 cm,
(ii) 8 dm 5 cm and 5 dm 6 cm.

Answer 1

(i)
Length of one diagonal = 16 cm
Length of the other diagonal = 28 cm
∴ Area of the rhombus = $\frac{1}{2}$ $\times$ (Product of the diagonals)
= $\left(\frac{1}{2}\times 16\times 28\right)$ cm² = 224 cm²
(ii)
Length of one diagonal = 8 dm 5 cm = (8 $\times$ 10 + 5) cm = 85 cm [since 1 dm = 10 cm]
Length of the other diagonal = 5 dm 6 cm = (5 $\times$ 10 + 6) cm = 56 cm
∴ Area of the rhombus = $\frac{1}{2}$ $\times$ (Product of the diagonals)
= $\left(\frac{1}{2}\times 85\times 56\right)$ cm²
= 2380 cm²