since the area of unshaded square = 49,
then side of unshaded square = 7 = width of shaded rectangles.

we cannot tell what is length & width of unshaded rectangle, but we can tell that its
length + width = 56/2 = 28

length of shorter shaded rectangle = width of unshaded rectangle
length of longer shaded rectangle = length of unshaded rectangle

therefore,
area of shaded parts = 28 x 7 = 196 cm2.
perimeter of shaded parts = 28+28+7+7+7+7 = 84 cm

Unshaded rectangle has the same length as the bottom shaded rectangle and its breadth is the same as the length of the right shaded rectangle.


So lengths of bottom shaded rectangle + lengths of right shaded rectangle

= Perimeter of unshaded rectangle
= 56cm

To get the perimeter of the shaded parts, we need to add in the respective breadths of the two rectangles

These are all 7cm since they are the same length as the square's sides
(√49 = 7 or 7 x 7 = 49)


So perimeter of shaded parts
= 56cm + 7cm x 4
= 56cm + 28cm
= 84cm

The other way you can see it :


The lengths and breadths of these 2 rectangles be separated and fitted onto the unshaded rectangle and the square.

So it is simply the sum of the perimeters of the square and the unshaded rectangle.

Also, these can all be transferred to the perimeter of the largest rectangle. This means that its perimeter is also 84cm.

For the area : (part a)

Area of bottom shaded rectangle

= breadth x length
= side of square x length of unshaded rectangle

= 7cm x length of unshaded rectangle


Area of right shaded rectangle

= breadth x length
= side of square x breadth of unshaded rectangle

= 7cm x breadth of unshaded rectangle


Combined area

= 7cm x length of unshaded rectangle
+ 7cm x breadth of unshaded rectangle

= 7cm x ( length + breadth of unshaded rectangle)


Since perimeter of unshaded rectangle = 2 breadth + 2 length = 56cm,

we divide by 2 to get 1 set of them.

1 breadth + 1 length = 56 cm ÷ 2 = 28cm


So, Combined area

= 7cm x 28 cm
= 196cm²

In short :

L - length of unshaded rectangle
B - breadth of unshaded rectangle

56cm = 2L + 2B
1L + 1B = 56cm ÷ 2 = 28cm

Side of square, S
= √49 cm = 7 cm
(Or 7cm x 7cm = 49cm²)


Combined area

= Area of bottom rectangle + area of right rectangle

= L x S + B x S
= L x 7 cm + B x 7 cm
= (L + B) x 7 cm
= 28 cm x 7 cm
= 196 cm²


Combined perimeter

= perimeter of bottom rectangle + perimeter of right rectangle

= 2L + 2S + 2B + 2S
= 2L + 2B + 4S
= 56 cm + 4 x 7 cm
= 84 cm