Question

Two segments, each 1 cm long, are marked on opposite sides of a square of side 8 cm.

The ends of the segments are joined.
What is the total shaded area?

Answer 1

Answer:

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Answer 2

Given: A square ABCD of side = 8cm

           Segment AO and DP = 1 cm each

To Find: Area of AOPD and OBCP

Solution:

• First we will consider area AOPD.

1. AO=DP= 1 cm (given)
2. AD=OP = 8 cm ( OP=BC)

• ∴ AOPD is a rectangle. Area of rectangle is given by

                           l × b             (1)    

where, l is length and

  and  b is breadth

Substituting values in formula for area we get:

area of AOPD = AO × OP

                        ⇒ 1 cm × 8 cm

                        ⇒ 8 $cm^{2}$              

• Now we consider the remaining area OBCP.
• As in case 1 above OBCP forms a rectangle with the dimensions:

1. OB=CP = 7 cm    (OB = AB - AO)
2. OP=BC = 8 cm  

Substituting values in equation (1) we get:

   Area of rectangle OBCP = OB × BC

                                           ⇒ 7 cm × 8 cm

                                           ⇒ 56 $cm^{2}$

Hence area of AOPD = 8 $cm^{2}$ and area of OBCP = 56 $cm^{2}$