Question

Find the perimeter and the area of the figure.

Answer 1

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the given figure is a composition of a rectangle as well as a right angled triangle !

we've been given the two sides of the rectangle and we're required to find out the height of the triangle , so as to find it's area ~

we know the the opposite sides of a rectangle are equal , therefore we can break the longest side ( length = 9.5 cm ) into two parts ! the first part of length = 7 cm which is the length of the rectangle and the rest 2.5 cm ( 9.5 - 7 = 2.5 ) will become the height of the triangle !

For perimeter of the figure -

$perimeter \: of \: figure = perimeter \: of \: rectangle + perimeter \: of \: triangle$

now ,

perimeter of rectangle = 2 ( l + b )

where ,

l = length

b = breadth

$\longrightarrow \: perimeter = 2(7 + 6) \\ \longrightarrow \: 2(13) \\ \longrightarrow \: 26 \: cm$

and ,

$perimeter \: of \: \triangle = 6.5 + 2.5 + 6 \\ \longrightarrow \: 15 \: cm$

Perimeter of figure in total = 26 cm + 15 cm

thus ,

$\qquad\quad\bold\red{perimeter \: = \: 41 \: cm}$

For area of the figure -

$area \: of \: figure = area \: of \: rectangle + area \: of \: rectangle$

now ,

area of rectangle = l × b

where ,

l = length

b = breadth

$area \: of \: rectangle = 7 \times 6 \\ \longrightarrow \: 42 \: cm {}^{2}$

and ,

$area \: of\triangle = \frac{1}{2} \times base \times height \\ \\ \longrightarrow \: \frac{1}{\cancel2} \times \cancel6 \times 2.5 \\ \\ \longrightarrow \: 3 \times 2.5 \\ \\ \longrightarrow \: 7.5 \: cm {}^{2}$

Area of figure in total = 42 cm² + 7.5 cm²

thus ,

$\qquad\quad\bold\red{Area \: = \: 49.5 \: cm^{2}}$

hope helpful :)

Answer 2

Step-by-step explanation:

perimeter = 7 + 6 + 9.5 + 6.5

= 29

area of rectangle = 6 X 7 = 42

area of triangle = ½ X 2.5. X 6 = 7.5

total area = 42 + 7.5 = 49.5