Answer: No, Kate can't completely cover the shape.
Explanation:
S=Area of Square. T=Area of each Triangle. A=Total Area
S=6*6
S=36 in^2
T=1/2 * 6 * 7.5
T=3*7.5
T=22.5 in^2
4T=4*22.5
4T=90 in^2
A=4T+S
A=90+36
A=126 in^2
120<126 ==> No, Kate can't completely cover the shape.