Question

This rectangular design is made from 6 squares. There are 2 small squares surrounded by 4 larger squares. The area of each small square is 1 cm^2.
What is the total area of the design?

Answer 1

Answer:

104 cm²

Step-by-step explanation:

Given area of small squares is 1 sq cm

so side AB = BC =CD = 1 cm

AC = AB + BC = 2cm

FD = FE + ED = 2 cm

GH = FD = 2 cm

But Given that FDHG is a square,

Since all sides are equal in a square

DH = FD = 2 cm

CH = CD + DH

= 1 + 2

Thus, CH = 3 cm

But AG = CH = PK = 3 cm

Given KAPG is a square, so

KP = KA = AG = PG = 3 cm

So, KC = KA + AC

= 3 + 2

= 5 cm

But given that SKCJ is  square,

so SK = KC = CJ = JS = 5 cm

JH = JC + CH

= 5 + 3

= 8 cm

Now, given that JHQR is a square

so JH = HQ = QR = RJ = 8 cm

Now, if we look at the rectangle PQRS

length of rectangle SR

= SJ + JR

= 5 + 8

= 13 cm

breadth of the rectangle SP

= SK + KP

= 5 + 3

= 8 cm

Area of rectangle PQRS

= PS * RS

= 13 * 8

= 104 cm²

Hope, it helps !

Answer 2

Answer:

Answer:

104 cm²

Step-by-step explanation:

Given area of small squares is 1 sq cm

so side AB = BC =CD = 1 cm

AC = AB + BC = 2cm

FD = FE + ED = 2 cm

GH = FD = 2 cm

But Given that FDHG is a square,

Since all sides are equal in a square

DH = FD = 2 cm

CH = CD + DH

= 1 + 2

Thus, CH = 3 cm

But AG = CH = PK = 3 cm

Given KAPG is a square, so

KP = KA = AG = PG = 3 cm

So, KC = KA + AC

= 3 + 2

= 5 cm

But given that SKCJ is  square,

so SK = KC = CJ = JS = 5 cm

JH = JC + CH

= 5 + 3

= 8 cm

Now, given that JHQR is a square

so JH = HQ = QR = RJ = 8 cm

Now, if we look at the rectangle PQRS

length of rectangle SR

= SJ + JR

= 5 + 8

= 13 cm

breadth of the rectangle SP

= SK + KP

= 5 + 3

= 8 cm

Area of rectangle PQRS

= PS * RS

= 13 * 8

= 104 cm²