Question

PLS HELP ME

26) Find the area of the figure.
A) 30cm^2
B) 36cm^2
C) 42cm^2
D) 48cm^2

Answer 1

Option B

Step by step explanation :

As we can see in figure, Triangle is right angled at A

In ∆ABC

By Pythagoras theorem,

BC² = AC² + AB²

=> BC² = (3)² + (4)²

=> BC² = 9 + 16

=> BC² = 25

=> BC = 5 cm

We know,

`\:\mathsf{Area \:of\: triangle}`=
`\:\mathsf{(1)/(2)\: x\: base\: x\: height}`

Here,

base = AC = 3cm

height = AB = 4cm

=>
`\:\mathsf{Area \:of\: triangle}`=
`\:\mathsf{(1)/(2) \:x\: 3cm\: x\:4cm}`

=>
`\:\mathsf{Area \:of\: triangle\: = \:3cm\: x\: 2cm}`

=>
`\:\bf\boxed{Area \:of\: triangle\: = \:6cm²}`

As BC = DE

And then BD = EC

it shows the property of rectangle

So BD = 6 cm

Now,

`\:\mathsf{Area \:of\: rectangle\: =\: length \:x\: width}`

=> Area of rectangle = 6cm x 5cm

=>
`\:\bf\boxed{Area\: of\: rectangle\: = \:30cm²}`

Now,

Area of the figure = Area of rectangle + Area of triangle

=> Area of the figure = 30cm² + 6cm²

=>
`\:\bf\boxed{Area\: of\: the\: figure\: = \:36cm²}`

Therefore, option B is the correct answer for this question.