Question

A rhombus sheet whose perimeter is 40m and diagnol is 12 m long is painted on both side at rate of rupees 5m°2.find the rate of painting

Answer 1

$\textbf{ Hello Mate! }$

As perimter of rhombus is 40 m

So, side = 40 m / 4 or 10 m

Its worth mentoning that a sheet rhombus in shape has to be painted both the sides. So, if the front side is divided into 2 triangles then whole paper (back side as well as front ) will have 4 triangles.

Area of on 1 traingle by Herons formula

$\sqrt{s(s - a)(s - b)(s - c)} \\ where \: s \: = \frac{a + b + c}{2} \\ s = \frac{10 + 10 + 12}{2} m = 16m \\ \sqrt{16(16 - 12)(16 - 10)(16 - 10)} \\ = \sqrt{ {2}^{4} \times {2}^{2} \times 6 \times 6 } \\ = (2 \times 2 \times 2 \times 6) {m}^{2} \\ = 48 {m}^{2}$
Then, area of whole paper = 48 m^2 × 4
= 192 m^2

Cost of painting 192 m^2 = 192 × 5
= Rs 960

$\boxed{ \textbf{ Answer : } Rs\:960 }$

Have great future ahead!