Question

3. Find the area of the polygon PQRSTUV as shown in the figure given below.
16 m
P
2 m
5 m
+5m->R
Q
3 m
S
- 6m-T​

Answer 1

Answer:

98

Step-by-step explanation:

Drop perpendiculars from R and U onto PV,

Let the foot of the perpendiculars onto PV be M and N respectively.

Area of polygon PQRSTUV can be dived into 3 regions:

1) Area of the square PQRM

2)Area of the rectangle MSTN

3)Area of the trapezium NTUV

Area of square PQRM = 5*5

=25 m²

Area of the rectangle MSTN

= (PQ+RS)*PV

= 8*6

=48 m²

Area of the trapezium NTUV

= 1/2h(a+b) where a and b are parallel sides and h is the height of the trapezium

h = NV = PV -PN

=16 - (PM + ST)

=16 - (QR + ST) (since PM = QR)

= 16 - 11

=5 m

Parallel sides are UV and NT which are 2 and 8.

hence, area = 5/2(2 +8)

=25 m.

Area of polygon =

25 + 48 + 25

=98 m²