Squares in a Rectangle

Let $A$ be the total area.

animation $\implies A = (5+4) \times (4 + 3) = \boxed{63}$

In the bottom right we have a square of size $3\times3$ , in the bottom left a $4\times4$ and in the upper left a $5\times5$ . Thus the area of the rectangle is $(3+4)\times(4+5)=63$ .

Extends all the lines and color them......Visualization is much easier

brown square=12 i.e area of brown=(2 2) 12=48 green square=15 i.e area of green=(1 1) 15=15 Therefore, area of the whole rectangle is =48+15=63

I hope this explains everything. :)

The shape can be divided into following shape.

There are 12 big squares of area 4.

There are 15 squares of area 1.

Total Area = 12 * 8 + 15 * 1

                     =48 + 15

                     = 63

There's one green square (1x1) and two squares congruent with the orange square (2x2). Bottom right square's side is the side of the green and the orange added together and a square so it's (3x3). Same process to get the bottom left square at 4x4 and 5x5 for the top left square. 25+16+9+4+4+4+1=63

(2 + 2 + 2 + 3)*(3 + 4) = 63 2 is the base of the upper square, and you have 3 of them. The base of the bottom right square is 2 + 1. You multiply by the base of the bottom right square plus the base of the lower left corner, which is 3 + 1

long side = 2*3 =6+3=9

breath side=3+4=7

therefore area= 9*7 = 63

Area= length × breadth

=[(2+2+2+3)×(3+4)]

=9×3

=63 Answer

( 6 + 3 ) × ( 4 + 3 ) = 9 × 7 = 63. Its easy if you DRAW first

(1x1)+3(2x2)+(3x3)+(4x4)+(5x5)=63

2 X 2 = Area of the brown box and the adjacent squares have equal sides so it becomes 4 X 3 (as the three adjacent squares have equal sides). The length of the sides increases from 1<2<3<4<5 which could be interpreted from the diagram so when you add 12 + 9 + 16 + 25 + 1(area of the squares) you get 63

Just looking like a square is not definitive proof that it is a square! So i think picture should be more explained and specified.

7*9=63 sq units

5 X 5 + 2 X 2 + 2 X 2 + 2 X 2 + 3 X 3 + 4 X 4 + 1 X 1 = 63

1) KC = IJ = IK = 1 + 2 = 3

2) DK = EF = FK = FI + IK = 1 + 3 = 4

DC = KC + DK = 3 + 4 = 7 (smaller side of rectangle)

BC = 3 * 2 + JC = 3 * 2 + KC = 3 * 2 + 3 = 9 (larger side of rectangle)

Area of the triangle = DC * BC = 63

given the way, the squares are placed around the 1cm square, we can see easily that: let a be the 2 cm square. and b,c,d the other squared, ordered by size.

then it's obvious that the sidelength of b, the next biggest square , is side length of a plus the 1 cm of the 1 cm square. same goes for b and c: c length=b length+1 d length=c length+1

we find that their lengths are: a=2,b=3,c=4,d=5

then we just need to square all the lengths and add them up, keeping in mind thatt there are 3 2cm squares: 1^2+2^2+2^2+2^2+3^2+4^2+5^2=63

The square at the bottom right has sides of $2 + 1 = 3$ . From this we can also deduce that the square at the bottom left has sides of $3 + 1 = 4$ .

Thus, the sides of the rectangle are $3 \times 2 + 3 = 9$ and $3 + 4 = 7$ . The area of the rectangle can now easily be calculated as $9 \times 7 = \large \color{#20A900}{\boxed{63}}$

Area of rectangle = right hand edge x bottom edge. = (2 + 2 + 2+ 3) x (3 + 4) = 63

Picture solution

A=(5+2)×(6+3)=63

Area of a rectangle=(length x breadth) So just count the number of boxes and extrapolate to estimate the length of each side and hence the area of the rectange which is (7[vertical] x 9 [horizontal]=63)

Area=(4+3)*(2+2+2+3)=63. Here 7 is the length which is obtained from the length of the sides of the squares......and 9 is the breath.....it is also obtained from the length of the sides of the squares and thus area is obtained.

it's 7x9=63 :)

Vertical distance=(2+2+2+3) and Horizontal distance (3+4). So, (2+2+2+3)×(3+4)=9×7=63

Length is (2+2+2+3) and width is (3+4). So area of rectangle is 9X7=63

4+4+4+1+9+16+25=63

Since the brown square has a side length of 2, and the green square a side length of 1, it follows that the largest square has a side length of 5. Similarly, adding the sides of brown and green gives us a side of 3 for the bottom - right square. Thus, the rectangle's width is 7, and the height 9. The total area therefore being 7 × 9 = 63

L = 2X3+2+1= 9, W = 3+2x2 = 7, Area = LxW = 9x7 = 63

The green has an area of 1, the brown has an area of four. There are three of those size, so 12 as total area. The big one has an area of 25, below it, 16, beside that, 9. Add it all up to 62

(2+2+2+3)x(3+4)=63