Question

Find the perimeter and the area of the figure.

Answer 1

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

Answer 2

`\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}`

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 * 6 \\ \longrightarrow \: 42 \: cm {}^(2)`

and ,

`area \: of\triangle = (1)/(2) * base * height \\ \\ \longrightarrow \: (1)/(\cancel2) * \cancel6 * 2.5 \\ \\ \longrightarrow \: 3 * 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 :)