Answer:
a). Yes. Area will be less than 100 square in.
b). Area of octagon = 82 in²
Step-by-step explanation:
From the picture attached,
a). Octagon is inscribed in a square having one side = 10 inches.
Since, octagon is obtained by cutting off the four equal corners of the square,
Area of octagon will be less than the area of the square.
Area of square = (side)²
= 10²
= 100 in²
Therefore, area of octagon will be less than 100 in²
b). Since, corner cut off from the square are equal in shape and area,
Area of one corner (right angle triangle) = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
= [tex]\frac{1}{2}(3)(3)[/tex]
= 4.5 in²
Area of 4 corners = 4.5 × 4 = 18 in²
Area of octagon = Area of square - Area of 4 corners removed
= 100 - 18
= 82 in²
