Question

find the area of a rhombus whose base =2.5 cm and height =13.5 cm

Answer 1

ABCD is a rhombus whose base AB = b, DB ⊥ AC DB = d₁ AC = d₂ and the altitude from C on AB is CE, i.e., h.

Area of rhombus ABCD = 2 Area of ∆ ABC

= 2 × 1/2 AB × CD sq units.

= 2 × 1/2 b × h sq. units

= base x height sq. units

Also, area of rhombus = 4 × area of ∆ AOB

= 4 × 1/2 × AO × OB sq. units

= 4 × 1/2 × 1/2 d₂ × 1/2 d₁ sq. units

= 4 × 1/8 d₁ × d₂ square units

= 1/2 × d₁ × d₂; where d₁ and d₂ are diagonals.

Therefore, area of rhombus = 1/2 (product of diagonals) square units

Answer 2

$base \: of \: rhombus = 2.5 \\ height \: of \: rhombus = 13.5 \\ area \: of \: rhombus = base \times height \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2.5 \times 13.5 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 33.75 {cm}^{2}$