2. ABCD is a square of side 2cm and E, F, G and H are the mid points of the side. AB, BC, CD and DA P, Q, R, S are mid points of EB, FC, GD, HA respectively. Find (area of square PQRS) ×25 is
Question
2. ABCD is a square of side 2cm and E, F, G and H are the mid points of the side. AB, BC, CD and DA P, Q, R, S are mid points of EB, FC, GD, HA respectively. Find (area of square PQRS) ×25 is
Solution
To solve this problem, we need to understand that the area of a square is given by the formula side^2.
Step 1: Find the side of the smaller squares.
Since E, F, G, and H are the midpoints of the sides of the square ABCD, the side of the smaller squares (like EABF) is half of the side of the larger square. So, the side of the smaller squares is 2cm/2 = 1cm.
Step 2: Find the side of the smallest square.
Similarly, since P, Q, R, and S are the midpoints of the sides of the square EFGH, the side of the smallest square (PQRS) is half of the side of the square EFGH. So, the side of the smallest square is 1cm/2 = 0.5cm.
Step 3: Find the area of the smallest square.
Using the formula for the area of a square (side^2), the area of the smallest square is (0.5cm)^2 = 0.25cm^2.
Step 4: Multiply the area of the smallest square by 25.
Finally, multiplying the area of the smallest square by 25 gives 0.25cm^2 * 25 = 6.25cm^2.
So, the area of square PQRS multiplied by 25 is 6.25cm^2.
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