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Given: PQR is a triangle X divides the base QR in the ratio of 2:1 i.e., QX= 1/2 XR rtp: ar triangle PQX =1/3ar triangle PQR construction: join PX draw an altitude PY for triangle PQR proof: area of triangle PQX = 1/2 *PY*QX area of triangle PXR = 1/2 * PY * XR = 1/2 * PY * 2QX = 2(1/2 * PY * QX) = 2( area of triangle PQX) we know that, area of triangle PQR = area of triangle PQX + area of triangle PXR = 3( area of triangle PQX) area of triangle PQX = 1/3(area of triangle PQR ) hence proved