Question

the given figure is the net of prism made up of four identical triangles and square. If the total area of the faces of the prisms 162cm square then find side of square ​

Answer 1

The side of the square $=9.67\ cm$

Step-by-step explanation:

Here the triangles are identical so we take it as equilateral triangles.

Area of an equilateral triangle $=\frac{\sqrt{3} }{4}(a)^2$,where $a$ is the measure of side length of the triangle.

Here we have $4$ triangles so total area of the face of the $4$ equilateral triangles.

Also we have to consider that the square on which all the triangles are lying is having the side length measures $a$ and is equivalent to the side length of the triangle.

So the side of the square $=a$

Then $4\times \frac{\sqrt{3} }{4}(a)^2={\sqrt{3}(a)^2=162\ cm^{2}$

Solving $a$ by removing the square roots.

We have

$a^{2}=\frac{162}{\sqrt{3}}=\frac{162 \sqrt{3}}{3}=54\sqrt{3}$

$a=\sqrt{54\sqrt3} =9.67\ cm$

So the side of the square, $=9.67\ cm$

Answer 2

Answer:

9

Step-by-step explanation:

let hight of the triangle to be h

and side of square to be a

Now , a+h+h = 18

h= (18-a)/2 = 9-(a)/2

so surface area of prism =162

area of square + 4*area of triangle =162

a*a +4* 1/2 *h*b =162

a² + 2a* (9-a/2)=162

a²+2a*9-2a*a/2 =162

a²+18a-a²=162

18a=162

a=162/18= 9

so side of square is 9