Question

The area of the parallelogram whose length is 30 cm, width is 20 cm and one diagonal is 40cm is

• A. $$200\sqrt{15}cm^2$$
• B. $$100\sqrt{15}cm^2$$
• C. $$300\sqrt{15}cm^2$$
• D. $$150\sqrt{15}cm^2$$

Answer 1

Answer:

$$150\sqrt{15}cm^2$$

.

In $\triangle{ ABD}$, AB = 20 cm. AD = 30cm. BD = 40 cm.

Semi–Perimeter (s)$=\frac{a+b+c}{2}$

$=\frac{20+30+40}{2}$

$=45cm$

Area of $\triangle{ABD} = \sqrt{s(s-a)(s-b)(s-c)}$

$=\sqrt{45(45-20)(45-30)(45-40)}$

$=\sqrt{45\times{25}\times{15}\times{5}}$

$=\sqrt{5\times{3}\times{3}\times{25}\times{3\times{5}}\times{5}}$

$=5\times{5}\times{3}\sqrt{15}$

$=75\sqrt{15}$sq.cm

Area of parallelogram ABCD $=2\times{75\sqrt{15}}$

$=150\sqrt{15}$ sq.cm