Question

the adjacent sides of parallelogram abcd measure 34cm and 20cm and the diagonal ac measure 42cm. find the area of parallelogram​

Answer 1

area = (34 × 20) cm

= 680 cm sq

Answer 2

$\huge\bold\blue{\underline{\underline{Answer!!}}}$

Let AB = 34cm and BC = 20cm can be adjacent sides of a parallelogram ABCD and the diagonal AC= 42cm divides it into two equal parts.

Let $\textbf{s}$ be the semi-perimeter of ∆ABC, then

s = $\sf\frac{AB+BC+CA}{2}$

s = $\sf\frac{34+20+42}{2}$ cm.

s = $\sf\frac{96}{2}$ = 48cm

• s - AB = (48-34)=14cm
• s - BC = (48-20)=28cm
• s - AC = (48-42) = 6cm.

$\therefore$ Area of ∆BAC $\implies$ $\sf\sqrt{(s-a)(s-b)(s-c)}$

$\implies$ $\sf\sqrt{48×14×28×6}$$\sf{cm}^{2}$

$\implies$$\sf\sqrt{3×16×14×14×2×2×3}$$\sf{cm}^{2}$

$\implies$$\sf\sqrt{2^2×3^2×4^2×14^2}$$\sf{cm}^{2}$

$\implies$ $\sf{(2×3×4×14)}$$\sf{cm}^{2}$

$\huge{\boxed{\boxed{336 cm^2}}}$

★ Area of parallelogram ABCD = 2 × Area of ∆ABC

= (2×336) cm².

= $\bf{672 cm^2}$