Question

Find the perimeter and total area of the compositor shape shown below. All measurements are given in inches.

Answer 1

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

Given :-

• The radius of the hemisphere is 3 units
• The height of the hemisphere is 3 units
• The height of the triangle is 4 units
• The other two sides of triangle is 5 units each

To Find :-

• We have to find the area and perimeter of the composite solid ?

Let's Begin :-

We have given one composite which is composed of hemisphere and triangle

We know that,

Perimeter of hemisphere

$\bold{\red{ = }}{\bold{\red{\pi{r}}}}$

Perimeter of the triangle

$\bold{\pink{ = S + S + S }}$

[ Both the figures have common base area ]

Therefore,

Total perimeter of the composite solid

$\sf{ = 5 + 5 + }{\sf{\dfrac{22}{7}}}{\sf{\times{r}}}$

$\sf{ = 10 + }{\sf{\dfrac{22}{7}}}{\sf{\times{3}}}$

$\sf{ = 10 + }{\sf{\dfrac{66}{7}}}$

$\sf{ = }{\sf{\dfrac{70 + 66}{7}}}$

$\sf{ = }{\sf{\dfrac{136}{7}}}$

$\bold{ = 19.42\: inches }$

Thus, The perimeter of the composite solid is 19.42 inches

Now,

We have to find the area of composite solid

We know that,

Area of hemisphere

$\bold{\blue{ = }}{\bold{\blue{\dfrac{1}{2}}}}{\bold{\blue{\pi{r²}}}}$

$\sf{ = 0.5}{\sf{\times{\dfrac{22}{7}}}}{\sf{\times{ 3 }}}{\sf{\times{ 3 }}}$

$\sf{ = 0.5}{\sf{\times}}{\sf{\dfrac{22}{7}}}{\sf{\times{ 9 }}}$

$\sf{ = 0.5}{\sf{\times{\dfrac{198}{7}}}}$

$\sf{ = }{\sf{\dfrac{99}{7}}}$

$\bold{ = 14.14\: inches }$

We also know that,

Area of triangle

$\bold{\purple{ = }}{\bold{\purple{\dfrac{1}{2}}}}{\bold{\purple{\times{ Base}}}}{\bold{\purple{\times{height }}}}$

Subsitute the required values,

$\sf{ = }{\sf{\dfrac{1}{2}}}{\sf{\times{ 4 }}}{\sf{\times{3}}}$

$\sf{ = 2 }{\sf{\times{ 3 }}}$

$\bold{ = 6\: inches }$

• [Note :- Both the figures have common base area. So for triangle base area will be 6/2 = 3 in.]

Therefore,

Total Area of the composite solid

$\sf{ = 14.14 + 6}$

$\bold{\red{ = 20.14\: inches }}$

Hence, The perimeter and area of composite solid is 19.42 inches and 20.14 inches .