Question

ABCD is a rectangle in which AB=30cm,and AD=20cm,.P is the mid point of AD.Q is the midpoint of AB, R is the midpoint of BC, S is the midpoint of DC. find the area of the shaded region​

Answer 1

Given:

• ABCD is a rectangle where AB=30 cm and AD=20 cm

• P is the mid point of AD, Q is the midpoint of AB, R is the midpoint of BC, S is the midpoint of DC.

To Find:  

• Find the area of the shaded region PQRS

Solution:

Area of rectangle $ABCD = length \times width$

                                          $= 30 \times 20$

                                         $= 600 cm^2$

Q is the midpoint of AB

                     $AQ =\frac{1}{2} \times 30$

                        $AQ =15cm$

R is the midpoint of BC

                   $BR =\frac{1}{2} \times 20$

                   $BR = 10 cm$

     Area of $\Delta PAQ = \frac{1}{2} \times B \times H$

      Area of $\Delta PAQ = \frac{1}{2} \times 15 \times 10$

      Area of $\Delta PAQ = 75 cm^2$

All four triangles in the rectangle ABCD are equal

So,

      Area of All 4 triangle = 4 × Area of  $\Delta PAQ$

      Area of 4 triangle $= 75 \times 4$

                             $= 300 cm^2$

                             

Area of shaded region PQRS = Area of rectangle ABCD - Area of 4 triangles

                                                 $=600 - 300\\= 300 cm^2$

Thus, Area of shaded region PQRS  $= 300 cm^2$

Answer 2

Step-by-step explanation:

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