Question

Consider a square of length 3 units. Also consider two points on each side of the square trisecting it into equal parts. The area of the octagon made by these eight points will be 

(a) 4 unit² 

(b) 6 unit² 

(c) 7 unit² 

(d) 8 unit² 

Answer 1

(c) 7 sq. units

Area of octagon ABHGDCFE 

= Area of rectangle ABDC + Area of trapezium BHGD + Area of trapezium ACFE

= (1× 3) + \(\frac12\) × (1 + 3) × 1 + \(\frac12\) × (1 + 3) × 1 

= 7 sq. units.