Question

The area of the figure ABCEFGA is 84 m². AH = HC = AG = 6 m and CE = HF = 4 m. If the angles marked in the figure are 90°, then the length of DB will be

(a) 2.5 m 

(b) 5 m 

(c) 6 m 

(d) 12 m

Answer 1

(b) 5 m

Area of rectangle CEFH + Area of trapezium FHAG 

= (4 × 6) m² + \(\bigg(\frac12\times(6+4)\times6\bigg)\)m² 

= 24 m² + 30 m² = 54 m² 

∴ Area of right angled ΔABC = 84 m² – 54 m² = 30 m² 

⇒ \(\frac12\)x 12 x BD = 30 ⇒ BD = 5 m.