Question

A rhombus shaped sheet with perimeter 40 cm and one diagonal 12 cm is painted on both side at the rate of 5 cm square find the cost of painting

Answer 1

ANSWER:-

Given:

A rhombus shaped sheet with perimeter 40cm & one diagonal 12cm is painted on both side at the rate of 5cm².

To find:

The cost of painting.

Solution:

We know that, In rhombus, all sides are equal.

•Perimeter= 40cm [given]

So,

•Perimeter of rhombus= 4 × side

=) 40 = 4 ×side

=) side= 40/4

=) side= 10cm

We have,

⚫a= 10cm

⚫b= 10cm

⚫c= 12cm

Therefore,

Using Heron's Formula, we get;

$= > s = \frac{a + b + c }{2} \\ \\ = > s = \frac{10 + 10 + 12}{2} \\ \\ = > s = \frac{32}{2} \\ \\ = > s = 16cm$

Now,

Area of ∆BCD,

$= > A = \sqrt{s(s - a)(s - b)(s - c)} \\ \\ = > \sqrt{16(16 - 10)(16 - 10)(16 - 12)} \\ \\ = > \sqrt{16(6)(6)(4)} \\ \\ = > \sqrt{2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 2 \times 3 \times 2 \times 2} \\ \\ = > 2 \times 2 \times 2 \times 2 \times 3 \\ \\ = > 16 \times 3 \\ \\ = > 48 {cm}^{2}$

As,

ABCD is a rhombus,

Ar.(∆BCD)= Ar.(∆ABD)

Area of rhombus (ABCD)

=) Ar.(∆BCD) + Ar.(∆ABD)

=) 48cm²+ 48cm²

=) 96cm²

•Cost of painting on both sides at the rate of Rs.5cm²

=) Rs. (5 × 2 × 96)

=) Rs.(10×96)

=) Rs.960

Hence,

The cost of painting is Rs.960.

Hope it helps ☺️