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{(1)/(2)}}}{\bold{\pink{*{ Base}}}}{\bold{\pink{*{ Height }}}}`

Subsitute the required values,

Area of 1 triangle

`\sf{=}{\sf{(1)/(2)}}{\sf{*{7}}}{\sf{*{ 6 }}}`

`\sf{ = 7 }{\sf{*{ 3 }}}`

`\sf{ = 21 cm^(2)}`

Therefore,

Area of 2 triangle's

`\sf{ = 2 }{\sf{*{ ( Area\:of\:1\:traingle) }}}`

`\sf{ = 2 }{\sf{*{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{*{ Breath }}}}`

Subsitute the required values,

Area of 1 rectangle

`\sf{ = 13.1 }{\sf{*{ 7 }}}`

`\sf{ = 91.7 cm^(2)}`

Therefore,

Area of 3 rectangles

`\sf{ = 3 }{\sf{*{( Area\:of\:1\:rectangle) }}}`

`\sf{ = 3 }{\sf{*{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 .