Respuesta :

Answer:

1) In fig. (1) there are 2 shapes:

  1. A Rectangle
  2. A triangle

So,

Area of Rectangle = l × b

where,

  • length (l) = 12 cm
  • breadth (b) = 14 cm

➮ 12 × 14

➮ 168

Hence, the area of rectangle is 168cm².

Now,

Area of Triangle = ½bh

where,

  • base (b) = 8 cm
  • height (h) = 12 cm

➮ ½ × 8 × 12

➮ ½ × 96

➮ 48

Hence, the area of triangle is 48cm².

Thus, Area of the whole fig. :

Area of Rectangle + Area of Triangle

➮ 168 + 48

➮ 216cm² (Ans)

2) In fig. (2) there are also 2 shapes :

  1. A Semicircle
  2. A Rectangle

So,

Area of Semicircle = ½ (πr²)

where,

  • pi (π) = 3.14
  • radius (r) = 5 inches

➮ ½ × 3.14 × (5)²

➮ ½ × 3.14 × 25

➮ ½ × 78.5

➮ 39.25

Hence, the area of semicircle is 39.25 in².

Now,

Area of Rectangle = l × b

where,

  • length (l) = 10 inches
  • breadth (b) = 15 inches

➮ 10 × 15

➮ 150

Hence, the area of rectangle is 150 in².

Thus, Area of whole fig. :

Area of Semicircle + Area of Rectangle

➮ 39.25 + 150

➮ 189.25 in² (Ans)

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Starrysoul100

[tex]\bold{\huge{\underline{ Solutions }}}[/tex]

Figure 1 :-

Given :-

  • We have one composite figure that is composed rectangle and triangle
  • The dimensions of rectangle are 12 cm and 14 cm
  • The dimensions of triangle are 12cm and 8cm

To Find :-

  • We have to find the area of composite figure

Let's Begin :-

We have,

  • Composite figure composed of rectangle and triangle

We know that,

Area of rectangle

[tex]\bold{ = Length {\times} Breath}[/tex]

  • The dimensions of rectangle are 12cm and 14cm

Subsitute the required values,

[tex]\sf{ = 12 {\times} 14}[/tex]

[tex]\sf{ = 168 \: cm^{2}}[/tex]

For triangle

Area of triangle

[tex]\bold{=}{\bold{\dfrac{ 1}{2}}}{\bold{ {\times} b{\times}h}}[/tex]

Subsitute the required values,

[tex]\sf{=}{\sf{\dfrac{ 1}{2}}}{\bold{ {\times}8{\times}12}}[/tex]

[tex]\sf{=}{\sf{\dfrac{ 1}{2}}}{\bold{ {\times} 96}}[/tex]

[tex]\sf{ = 48 \:cm^{2}}[/tex]

Thus, Area of triangle is 48 cm² .

Therefore,

The total area of the composite figure

= Area of rectangle + Area of triangle

[tex]\sf{ = 168 + 48}[/tex]

[tex]\bold{ = 216\: cm^{2}}[/tex]

Hence, The area of given composite figure is 216 cm²

Figure 2 :-

Given :-

  • We have one composite figure which is composed of semicircle and rectangle
  • The dimensions of rectangle are 10 in. and 15 in.
  • The diameter of semicircle is 10 in.

Let's Begin :-

Here, we have

  • Composite figure composed of rectangle and hemisphere

We know that,

Area of rectangle

[tex]\bold{ = Length {\times} Breath}[/tex]

  • The dimensions of rectangle are 10in. and 15 in.

Subsitute the required values,

[tex]\sf{ = 10 {\times} 15}[/tex]

[tex]\sf{ = 150 \: cm^{2}}[/tex]

For hemisphere

Area of semicircle

[tex]\bold{ = 1/2{\pi}r^{2}}[/tex]

  • The diameter of hemisphere is 10 in.
  • So, The radius of hemisphere will be 5 in. as it is the half of diameter.

Subsitute the required values,

[tex]\sf{ =}{\sf{\dfrac{ 1}{2 }}}{\sf{ {\times} 3.14 {\times} (5)^{2}}}[/tex]

[tex]\sf{ = }{\sf{\dfrac{1}{2}}}{\sf{ {\times}3.14 {\times} 25}}[/tex]

[tex]\sf{ = 1.57 {\times} 25}[/tex]

[tex]\sf{ = 39.25\: in^{2}}[/tex]

Thus, The area of semicircle is 39.25 in².

Therefore,

Total area of the given composite figure

= Area of hemisphere + Area of rectangle

= [tex]\sf{ = 150 + 39.25}[/tex]

[tex]\bold{ = 189.25\: in^{2}}[/tex]

Hence, The total area of the given composite figure is 189.25 in² .