Triangles or polygons from points on the sides of a figure
This type of question, asked 5 times: 2021 Paper 6, 2021 Paper 8, 4 Apr 2024, 3 Apr 2025, 22 Jan 2026 S1. All 5 questions below, oldest first.
Try each one first, then open its answer.
Question 1
2021 Paper 6
71Consider a rectangle having 5, 7, 6, 9 points in the interior of the line segments , respectively. Let be the number of triangles having these points from different sides as vertices and be the number of quadrilaterals having these points from different sides as vertices. Then is equal to:Tap an option to check your answer.
Question 2
2021 Paper 8
71If the sides and of a triangle have 3,5 and 6 interior points respectively, then the total number of triangles that can be constructed using these points as vertices, is equal to:Tap an option to check your answer.
Question 3
4 Apr 2024
68There are 5 points on the side , excluding and , of a triangle . Similarly, there are 6 points on the side and 7 points on the side of the triangle. The number of triangles, that can be formed using the points as vertices, is:Tap an option to check your answer.
Question 4
3 Apr 2025
133Line of slope 2 and line of slope intersect at the origin O . In the first quadrant, are 12 points on line and are 9 points on line . Then the total number of triangles, that can be formed having vertices at three of the 22 points , , is:Tap an option to check your answer.
Question 5
22 Jan 2026 S1
75Let ABC be a triangle. Consider four points , on the side AB , five points on the side BC and four points on the side AC . None of these points is a vertex of the triangle ABC . Then the total number of pentagons, that can be formed by taking all the vertices from the points , is .