Can you Solve this math problem and explain how?

Question

first draw two axis (x,y) then install these points: A (1,0) B (2,2) C (5,6) D (7,5) E (9,0).
Now calculate the area of ABCDE in square units.

Answer 1

First take a graph paper, then install those points. Join them with each other. Now you get a polygon having 5 sides. Name the points as A,B,C,D,E as you mentioned. Now join B, C and D to the side AE perpendicularly at P, Q and R respectively. Now you are getting 4 seperate figures viz. ABP as right triangle, BCQP and CDRQ as trapezia, DER as right triangle again. As the co-ordinates are given, you will get lengths as follows:
AP = 1
BP = 2
PQ = 3
CQ = 6
QR = 2
DR = 5
RE = 2

Now, in Triangle ABP, Area = base X height / 2
= AP x BP / 2
= 1 X 2 / 2
= 1 sq. units ------------------ (1)

In trapezium BCQP, Area = height X (side1+side2) / 2
= PQ x (PB + QC) / 2
= 3 x (2 + 6) / 2
= 12 sq. units -------------------- (2)

Similarly, trapezium CDRQ, Area = QR X (QC + RD) / 2
= 2 X (6 + 5) / 2
= 11 sq. units ---------- (3)

In right triangle DER, Area = base X height / 2
= DR X RE / 2
= 5 X 2 / 2
= 5 sq. units -------------------- (4)

Now, Total Area of the polygon ABCDE = (1) + (2) + (3) + (4)
= 1 + 12 + 11 + 5
= 29 sq. units

Hoping you got it. If any problem, contact me on [e-mail]

Answer 2

Draw the figure and solve the enclosed
right triangles for area.