Question 52

$$\triangle$$ABC and $$\triangle$$XYZ are equilateral triangles of 54 cm sides. All smaller triangles like $$\triangle$$ANM, $$\triangle$$OCP, $$\triangle$$QPX etc. are also equilateral triangles. Find the area of the shape MNOPQRM.

Solution

AB = 54 cm and $$\triangle$$ANM , $$\triangle$$OCP , $$\triangle$$OPX are equilateral triangles.

=> MN = MR = NO = OP = PQ = QR = $$\frac{54}{3} = 18$$ cm

Thus, MNOPQRM is a regular hexagon with side 18 cm

$$\therefore$$ Area of MNOPQRM = $$\frac{3 \sqrt{3}}{2} (side)^2$$

= $$\frac{3 \sqrt{3}}{2} \times 18^2 = 486 \sqrt{3} cm^2$$

Share on Whatsapp Share on Whatsapp

Create a FREE account and get:

XAT Quant Questions | XAT Quantitative Ability

XAT Exam

XAT Syllabus

XAT Admit Card

XAT Cutoffs

XAT Eligibility Criteria

XAT Exam Dates

XAT Colleges List

XAT Registration

XAT Result

XAT Previous Year Papers

XAT 2025 Crash Course

XAT Mock Tests