1. The area of square PQRS is 36 sq cm find the area of the square joining the mid-point of the sides of PQRS.
Answers
Area of a square PQRS = (Side)² = 36 cm² = 6²
PQ=QR=RS=SP=6 cm
Let P is the midpoint of PQ, B is the midpoint of QR, C is the midpoint of RS and D is the midpoint of SP.
To evaluate the area of square ABCD, find value of AB.
In △ABQ
AQ=1/2 ×PQ = 6/2 = 3 cm and
QB=1/2 ×QR = 6/2 = 3 cm
AB²=AQ²+BQ²=(3)²+(3)²=9+9=18=(3√2)²
Or, AB = 3√2 cm
AB=BC=CD=DA=3√2 cm
Area of the square ABCD = (Side)² = (3√2)² = 18 cm²
Therefore, Area of the square ABCD = 18 cm²
hope this helps you....
Answer:
Area of a square PQRS = (Side)² = 36 cm² = 6²
PQ=QR=RS=SP=6 cm
Let P is the midpoint of PQ, B is the midpoint of QR, C is the midpoint of RS and D is the midpoint of SP.
To evaluate the area of square ABCD, find value of AB.
In △ABQ
AQ=1/2 ×PQ = 6/2 = 3 cm and
QB=1/2 ×QR = 6/2 = 3 cm
AB²=AQ²+BQ²=(3)²+(3)²=9+9=18=(3√2)²
Or, AB = 3√2 cm
AB=BC=CD=DA=3√2 cm
Area of the square ABCD = (Side)² = (3√2)² = 18 cm²
Therefore, Area of the square ABCD = 18 cm²
Step-by-step explanation: