Question

ABCD is a square with area 64m². E,F,G and H are points on sides AB,BC,CD and DA, respectively,such that AE=BF=CG=DH=2m.E,F,G and H are connected to form square EFGH determine the area of EFGH​. ABCD is a square with area 64m². E,F,G and H are points on sides AB,BC,CD and DA, respectively,such that AE=BF=CG=DH=2m.E,F,G and H are connected to form square EFGH determine the area of EFGH​.

Answer 1

The area of square EFGH within the larger square ABCD is found to be 16m² by subtracting the known segments from ABCD's side and squaring the resulting length.

Step-by-step explanation:

To determine the area of square EFGH which is formed inside the larger square ABCD with area 64m², we first need to find the side length of square ABCD. Knowing the area is 64m² and that the area of a square is calculated by squaring the side length (area = side²), we can deduce that each side of square ABCD is 8m (since 8² = 64). Since AE=BF=CG=DH=2m, the side length of square EFGH is 8m - 2m - 2m = 4m, because we subtract the lengths AE and DH from one side of the larger square ABCD to find the side length of EFGH. Now, we can calculate the area of square EFGH by squaring its side length (area = side²), which gives us an area of 4m × 4m = 16m².