Question

What is the area of this figure​

Answer 1

`\large\boxed{A=54}`

Explanation:

Look at the picture.

We have two triangles and the trapezoid.

The formula of an area of a triangle:

`A_(triangle)=(bh)/(2)`

b - base

h - height

The formula of an area of a trapezoid:

`A_(trapezoid)=(b_1+b_2)/(2)\cdot h`

b₁, b₂ - bases

h - height

Triangle 1:

b = 3, h = 2

`A_1=((3)(2))/(2)=3`

Triangle 2:

b = 6, h = 1

`A_2=((6)(1))/(2)=3`

Trapezoid:

b₁ = 7, b₂ = 9, h = 6

`A_3=(7+9)/(2)\cdot6=(16)/(2)\cdot6=(8)(6)=48`

The area of the figure:

`A=A_1+A_2+A_3\\\\A=3+3+48=54`

Answer 2

Area of total structure = 54

Explanation:

We will calculate the area of figure 1 + 2 + 3 + 4 in the given structure to calculate the total area.

For triangle 1

Area of 1 = 1/2 × 2 × 3 = 3

For triangle 2

Area of 2 = 1/2 × 6 × 1 = 3

For triangle 3

Area of 3 = 1/2 × 2 × 6 = 6

For rectangle 4

Area of 4 = 7 × 6 = 42

Total area = area of 1 + area of 2 + area of 3 + area of 4

= 3 + 3 + 6 + 42 = 54

So the area of the figure is 54.