Answer:
Total area of the fabric = 66 in.²
Step-by-step explanation:
The diagram of the stretched fabric shown takes the shape of a kite having two diagonals that intersect each other.
Total area of the fabric = area of the kite = ½(product of the two diagonals)
= ½(AC × BD)
We need to find AC and BD
BE = DE = 6 in. (Equal lengths)
BD = BE + DE
BD = 6 + 6 = 12 in.
AC = AE + CE
Apply Pythagorean theorem to find AE and CE
✔️AE = √(AB² - BE²) = √((√45)² - 6²) = √(45 - 36) = √9 = 3 in.
✔️CE = √(CD² - DE²) = √(10² - 6²) = √(100 - 36) = √64 = 8 in.
FIND AC:
✔️AC = AE + CE
AC = 3 + 8
AC = 11 in.
FIND the total area of the fabric:
✔️Total area = ½(AC × BD) = ½(11 × 12)
= ½(132)
= 66 in.²
