Question

Someone please help me this is really confusing

Answer 1

Area of trapezoid is:
`\mathbf{11x^3y^2}`

Area of triangle is:
`\mathbf{6a^3b^2}`

Perimeter of triangle is:
`\mathbf{3ab+14a^2b}`

Explanation:

Image 1:

We need to Find area of trapezoid.

The formula used is:
`Area=(1)/(2)h(b_1+b_2)`

where h is height and b₁ and b₂ are parallel sides.

Looking at the figure we get:

h = 2xy

b₁ = 4x²y

b₂ = 7x²y

Putting values and finding area:

`Area=(1)/(2)h(b_1+b_2)\\Area=(1)/(2)* 2xy(7x^2y+4x^2y)\\Area=(1)/(2)* 2xy(11x^2y)\\Area=(1)/(2)* 22x^3y^2\\Area=11x^3y^2`

So, Area of trapezoid is:
`\mathbf{11x^3y^2}`

Image 2:

We need to find area and perimeter of triangle.

First we will find area of triangle.

The formula used is:
`Area=(1)/(2)* b * h`

where b is base and h is height

Looking at the figure,

b = 3ab

h = 4a²b

Finding area:

`Area=(1)/(2)* b * h\\Area=(1)/(2)* 3ab * 4a^2b\\Area=(1)/(2)* 12a^3b^2\\Area=6a^3b^2`

So, Area of triangle is:
`\mathbf{6a^3b^2}`

Now, finding Perimeter of triangle

The formula used is:
`Perimeter = Sum\:of\:lengths\:of\:all\:sides\:of\:triangle`

Looking at figure:

Length of side 1 = 3ab

Length of side 2 = 4a²b

Length of side 3 = 10a²b

Finding Perimeter

`Perimeter = Sum\:of\:lengths\:of\:all\:sides\:of\:triangle\\Perimeter = 3ab+10a^2b+4a^2b\\Perimeter=3ab+14a^2b`

So, Perimeter of triangle is:
`\mathbf{3ab+14a^2b}`