Question

Find the area of the two following figures for C and D

Answer 1

Answer:

Step-by-step explanation:

C. AB = AC-EF = 13-7= 6 cm

BD = CF-DE = 16-8=8 cm

triangle ABD=

By Pythagoras's Theorem

$AB^{2} + BD^{2} =AD^{2}$

$6^{2} +8^{2} =AD^{2}$

$36+64=AD^{2} \\100=AD^2 \\AD=10 cm$

Answer 2

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$\rightarrow$ Figure (c)

It is the figure with a combination of a Right angled triangle and a Rectangle.

So, we find area of both triangle and rectangle.

After That we will add both the areas.

(i) Right angled Triangle

$\color{red} {Formula\:used}$ = $\frac{1}{2}$ $\color{green} {Base\:×\:height}$

By observation we see,

Given :

• $\color{red} {Base}$ = 16 - 8 = 8cm

• $\color{red} {height}$ = 13 - 7 = 6cm

By this, we have found base and height of the triangle that is 8cm and 6cm respectively.

To Find :

• Area of the triangle

Solution :

$\star$Calculations

$\sf\huge\implies$ $\frac{1}{2}$ × Base × Height

By substituting values,

$\sf\huge\implies$ $\frac{1}{2}$ × $\color{red} {8}$cm × $\color{red} {6}$ cm

$\sf\huge\implies$ $\color{red} {24}$ cm²

(ii) Rectangle

$\color{red} {Formula\:used}$ = $\color{green} {2\:×\:(\: length\:+\: breadth}$

By observation we have,

• $\color{red} {Length}$ = $\color{green} {16cm}$

• $\color{red} {breadth}$ = $\color{green} {7cm}$

By this , We have found length and breadth that is 16 cm and 7cm respectively.

To find :

• Area of Rectangle

$\star$Calculations :

$\sf\huge\implies$ $\color{red} {Formula\:used}$ = $\color{green} {2\:×\:(\: length\:+\: breadth}$

By substituting values,

$\sf\huge\implies$ 2 × (16cm + 7cm)

$\sf\huge\implies$ 2 × (23cm)

$\sf\huge\implies$ 46cm²

$\therefore$ Area of Rectangle is 46cm²

To find area of polygon :

$\huge\sf\rightarrowtail$ Area of triangle + Area of Rectangle

By substituting values,

$\sf\huge\implies$ 46cm² + 24cm²

$\sf\huge\implies$ 70cm²

Hence , area of given polygon is 70cm²

___________________________

Figure (d)

As,we can se in figure (d) , it is the combination of two Rectangles

So, we fill find area of both Rectangles and then add them.

(i)To find area of Rectangle

Given :

• Length = 14 cm

• breadth = 4 cm

To Find :

• Area of reactangle (i)

Solution :

$\color{red} {Formula\:used}$ = $\color{green} {2\:×\:(\: length\:+\: breadth}$

$\star$ Calculations :

By substituting values,

$\sf\huge\implies$ 2 × ( 14 cm + 4cm)

$\sf\huge\implies$ 2 × (18cm)

$\sf\huge\implies$ 36cm²

Hence, area of Rectangle (i) is 36cm²

To find area of Reactangle (ii)

$\color{red} {Formula\:used}$ = $\color{green} {2\:×\:(\: length\:+\: breadth}$

Given :

• Length = 14 - (4 + 4) = 14 - 8 = 6cm

• Breadth = (7 - 4) = 3 cm

By observation we have,

$\color{red} {Length}$ = $\color{green} {6cm}$

$\color{red} {breadth}$ = $\color{green} {3cm}$

By this , We have found length and breadth that is 6 cm and 3cm respectively.

To find :

Area of Rectangle

$\star$Calculations :

$\sf\huge\implies$ $\color{red} {Formula\:used}$ = $\color{green} {2\:×\:(\: length\:+\: breadth}$

By substituting values :

$\sf\huge\implies$ 2 × (6cm + 3cm)

$\sf\huge\implies$ 2 × (9cm)

$\sf\huge\implies$ 18cm²

$\therefore$ Area of Rectangle (ii)

is 18cm²

To find area of polygon:

We will add area of Rectangle (i) and (ii)

By substituting values,

$\sf\huge\implies$36cm² + 18cm²

$\sf\huge\implies$ 44cm²

Hence, area of polygon is 44cm²