Previous Year Questions

In APQR, M, N, and S are the mid-points of sides PQ, PR, and QR, respectively. The area of ΔPORis 46 cm².

we know that:-

The area of a triangle formed by joining the mid-points of two sides of a triangle is one-fourth the area of the original triangle.

The area of the quadrilateral formed by mid-points of sides and one vertex is half the area of the original triangle.

so procedding with above formula:-

The mid-points M, N, and S divide ΔPQR into four smaller triangles of equal area.

Area of ΔPOR =46 cm²

Area of each smaller triangle = 46 /4

= Area of each smaller triangle = 11.5cm²

The quadrilateral MNRQ consists of three of these smaller triangles.

Area of quadrilateral MNRQ =3 X 11.5=34.5cm²

Option (d) is the correct answer.