Question

A rhombus-shaped sheet with perimeter 40cm and one diagonal 12 cm, is painted on

both sides at the rate of Rs. 5 per m2

. Find the cost of painting.​

Answer 1

$\bigstar \underline{ \: \underline{ \large \red{ \frak{Proper \: question}}}}$

A rhombus shaped sheet with perimeter 40 cm and one diagonal 12 cm, is painted on both sides at the rate of Rs 5 per m². Find the cost of painting.

Given,

• Perimeter = 40cm

• One diagonal = 12cm

• Painted price = Rs.5 per m²

To find,

• Find the cost of painting

$\bigstar \underline{ \frak{Solution}}$

In a rhombus, all sides are equal.

$\sf \: Perimeter \: of \: rhombus = 40 cm \\ \sf \: Side \: of \: rhombus = \frac{ \cancel{40}}{ \cancel{10}} = 10 cm$

a = 10, b = 10, c = 12

$\qquad \frak{\red {\: \boxed { \frak S = \frac{(a + b + c)}{2} }}}$

$\sf \: ⇒ s = \frac{ (10 + 10 + 12)}{2} \\ \sf S = \frac{ \cancel{32}}{ \cancel2} \\ \frak{ \red{ S= 16}. }$

$\sf \: Area \: (ΔBCD) = \sqrt{s(s-a)(s-b)(s-c)}$

$\sf \: ⇒ Area(ΔBCD) = \sqrt{16(16-10)(16-10)(16-12) }$

$\sf \: ⇒ Area(ΔBCD) = \sqrt{16×6×6×4 }$

$\sf \: ⇒ Area(ΔBCD) = 48 cm {}^{2}$

$\sf \: As \: ABCD \: is \: a \: rhombus, \: Area(ΔBCD) = Area(ΔABD)$

$\red {{ \boxed{\frak{⇒ Area \: of \: rhombus \: ( \sf{ABCD}) = \frak{Area} \: ( \sf{ \sf{ΔBCD }}) + \frak{ Area}}(ΔABD)}}}$

$\sf \: ⇒ Area \: of \: rhombus(ABCD) = 48 + 48$

$\sf \: \boxed{ \frak{ ⇒ Area \: of \: rhombus(ABCD) = 96cm2}}$

Now,

Cost of painting 1 m² = 5 per m²

Cost of painting 96m² = 96 × 5 = 480

Hence, the cost of painting rhombus - shaped sheet be Rs. 480

Answer 2

$\sf{In \: a \: rhombus \: , all \: \: sides \: are \: equal.}$

$\sf{Perimeter \: of \: rhombus = 40 cm}$

$\sf{Side \: of \: rhombus}$

$\sf = \frac{40}{4}$

$\sf{= 10 cm}$

$\sf{a = 10, b = 10, c = 12}$

So,

$\sf ⟹ \frac{a + b + c}{2}$

$\sf⟹ \frac{10 + 10 + 12}{2}$

$\sf⟹ \frac{32}{2}$

$\sf⟹ 16$

$\sf{Area :-}$

$\sf⟹ \sqrt{s(s - a)(s - b)(s - c)}$

$\sf⟹ area \: (Δabcd) = \sqrt{16(16 - 10)(16 - 10)(16 - 12)}$

$\sf⟹area (Δabcd) = \sqrt{16 \times 6 \times 6 \times 4}$

$\sf⟹ area (Δabcd) = {48cm}^{2}$

$\sf{As \: ABCD \: is \: an \: Rhombus \: , Area \: (ΔBCD) = (ΔABD)}$

$\sf{Area \: of \: Rhombus (ABCD) = Area (ΔBCD) + Area (ΔABD)}$

$\sf{Area \: of \: Rhombus \: ABCD = 48 + 48 }$

$\sf{Area \: of \: Rhombus \: ABCD = \: {96cm}^{2}}$

$\sf⟹ Hence \: the \: Answer \: is \: {96cm}^{2}$

So,

Cost of painting 1 m² = 5 per m²

Cost of painting 1 m² = 5 per m²Cost of painting 96m²

⟹ 96 × 5

⟹480

Hence, the cost of painting rhombus - shaped sheet be Rs. 480.