Question

@Michele_Laino

Answer 1

where is the question, please?

Answer 2

in order to compute the requested area, we have to subdivide such polygon into more triangles or rectangles, like below:

Answer 3

as we can see , I have subdivided such polygon, into four tringles and one rectangle

Answer 4

now, for example, the area of traingle T1, is:
\((3 \times 1) /2=...?\)

Answer 5

1.5

Answer 6

ok!
area of T2:
\((5 \times 1)/2=...?\)

Answer 7

2.5

Answer 8

ok! Next:
area of T3
\((4 \times 1)/2=...?\)

Answer 9

2

Answer 10

then, area of T4:
\[\frac{{4 \times 3}}{2} = ...?\]

Answer 11

6

Answer 12

and area of rectangle R1:
\[3 \times 4 = ...?\]

Answer 13

12

Answer 14

great!
So, the area of the polygon, is:
\(1.5+2.5+2+6+12=...?\)

Answer 15

24

Answer 16

that's right! :)

Answer 17

yes! Please look at this drawing:

Answer 18

first step:
the area of the rectangle ABCD, is:
\[7 \times 4 = ...?\]

Answer 19

28

Answer 20

great!
now, we have to compute the areas of each of triangles T1, T2, and T3

Answer 21

so, area of T1:
\[\frac{{4 \times 2}}{2} = ...?\]

Answer 22

4

Answer 23

ok!
area of T2:
\[\frac{{7 \times 3}}{2} = ...?\]

Answer 24

10.5

Answer 25

then area of triangle T3:
\[\frac{{5 \times 1}}{2} = ...?\]

Answer 26

2.5

Answer 27

correct!
Now, the area of the blue triangle, is given by subtracting, from the area of the rectangle ABCD, the areas of each triangles T1, T2, T3, namely, we have to do such computation:

\(28-(4+10.5+2.5)=...?\)

Answer 28

11

Answer 29

that's right! :)