Question

What is the area of this figure​

Answer 1

Answer:

Area of total structure = 54

Step-by-step 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.

Answer 2

Answer:

$\large\boxed{A=54}$

Step-by-step explanation:

Look at the picture.

We have two triangles and the trapezoid.

The formula of an area of a triangle:

$A_{triangle}=\dfrac{bh}{2}$

b - base

h - height

The formula of an area of a trapezoid:

$A_{trapezoid}=\dfrac{b_1+b_2}{2}\cdot h$

b₁, b₂ - bases

h - height

Triangle 1:

b = 3, h = 2

$A_1=\dfrac{(3)(2)}{2}=3$

Triangle 2:

b = 6, h = 1

$A_2=\dfrac{(6)(1)}{2}=3$

Trapezoid:

b₁ = 7, b₂ = 9, h = 6

$A_3=\dfrac{7+9}{2}\cdot6=\dfrac{16}{2}\cdot6=(8)(6)=48$

The area of the figure:

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