Question

What is the total surface area of the figure below?

Answer 1

$\bold{\huge{\pink{\underline{ Solution }}}}$

Given :-

• We have given one irregular figure which is composed 2 triangle's and 3 rectangles
• The height and base of the triangles is 6cm and 7 cm each
• The length and breath of the rectangles is 13.1 cm and 7cm each

To Find :-

• We have to find the total surface area of the given figure?

Let's Begin :-

We have,

• 2 triangles of height 6 cm and base 7cm each
• 3 rectangles of length 13.1 cm and 7cm each

Therefore ,

We know that,

Area of triangle

$\bold{=}{\bold{\pink{\dfrac{1}{2}}}}{\bold{\pink{\times{ Base}}}}{\bold{\pink{\times{ Height }}}}$

Subsitute the required values,

Area of 1 triangle

$\sf{=}{\sf{\dfrac{1}{2}}}{\sf{\times{7}}}{\sf{\times{ 6 }}}$

$\sf{ = 7 }{\sf{\times{ 3 }}}$

$\sf{ = 21 cm^{2}}$

Therefore,

Area of 2 triangle's

$\sf{ = 2 }{\sf{\times{ ( Area\:of\:1\:traingle) }}}$

$\sf{ = 2 }{\sf{\times{21 }}}$

$\sf{ = 42 cm^{2}}$

Thus, The area of 2 triangles is 42 cm²

Now,

We know that,

Area of rectangle

$\bold{\red{ = Length }}{\bold{\red{\times{ Breath }}}}$

Subsitute the required values,

Area of 1 rectangle

$\sf{ = 13.1 }{\sf{\times{ 7 }}}$

$\sf{ = 91.7 cm^{2}}$

Therefore,

Area of 3 rectangles

$\sf{ = 3 }{\sf{\times{( Area\:of\:1\:rectangle) }}}$

$\sf{ = 3 }{\sf{\times{91.7 }}}$

$\sf{ = 275.1 cm^{2}}$

Thus, The area of 3 rectangle is 275.1 cm²

So,

Total area of the given figure

• = Area of 2 triangles + Area of 3 rectangles

$\sf{ = 42 + 275.1 }$

$\bold{ = 317.1 cm^{2}}$

Hence, The total surface area of the given figure is 317.1 cm² .