The formula for the area, $$A$$ square cm of the white cross is\n \n \n \n \n A. $$A = 4ax + 4ay + {a^2}$$B. $$A = 2ax + 4ay + {a^2}$$C. $$A = 2ax + 2ay + {a^2}$$D. $$A = 4ax + {a^2}$$

Question

The formula for the area, $$A$$ square cm of the white cross is\n    \n    \n    \n    \n  A. $$A = 4ax + 4ay + {a^2}$$B. $$A = 2ax + 4ay + {a^2}$$C. $$A = 2ax + 2ay + {a^2}$$D. $$A = 4ax + {a^2}$$

Vedantu Content Team · Accepted Answer

Hint: First, we will find the length of the sides of a big square and small squares. Then we will use the area of square \[A = {x^2}\], where \[x\] is the length of the side of the square. Then we will find the area of the white cross by subtracting the area of four small squares from the area of the big square.

Complete step-by-step answer:
Given that the length of the side of small squares is \[x\] cm each.

First, we will find the length of the side of the big square from the given diagram.

\[x + a + x = 2x + a{\text{ cm}}\]

We know that the area of a square is \[{x^2}\], where \[x\] is the side of a square.

We will now find the area of the big square by using the above length of the side of the big square.

\[
  {\text{Area of big square }} = {\left( {2x + a} \right)^2} \\
   = 4{x^2} + 4ax + {a^2}{\text{ c}}{{\text{m}}^2} \\
\]

We will now calculate the area of a small square with a length of side \[x\] cm.

\[{\text{Area of small square}} = {x^2}{\text{ c}}{{\text{m}}^2}\]

Since there are 4 squares in the given diagram, we will multiply the area of the small square by 4 to find the area of four small squares.

\[
  {\text{Area of four small squares}} = 4 \times {x^2}{\text{ }} \\
   = 4{x^2}{\text{ c}}{{\text{m}}^2} \\
\]

Subtracting the area of four small squares from the area of the big square to find the area of white cross \[A\].

\[
  {\text{Area of white cross }}A = {\text{Area of big square}} - {\text{Area of four small squares}} \\
   = 4{x^2} + 4ax + {a^2} - 4{x^2} \\
   = 4ax + {a^2} \\
\]

Thus, the formula for the area \[A\] square cm of the white cross is \[4ax + {a^2}\].

Hence, option D is correct.

Note: In this question, the student should examine the length of the sides of the squares and cross from the diagram properly. The values should be written in the formula of area for big square and small squares appropriately.

The formula for the area, \[A\] square cm of the white cross is A. \[A = 4ax + 4ay + {a^2}\]B. \[A = 2ax + 4ay + {a^2}\]C. \[A = 2ax + 2ay + {a^2}\]D. \[A = 4ax + {a^2}\]

The formula for the area, \[A\] square cm of the white cross is

A. \[A = 4ax + 4ay + {a^2}\]
B. \[A = 2ax + 4ay + {a^2}\]
C. \[A = 2ax + 2ay + {a^2}\]
D. \[A = 4ax + {a^2}\]