Cross-Section of a Triangular Prism

Concept: If we slice a uniform solid parallel to its base, the resulting face is called a cross-section. Because a prism has a uniform shape throughout its length, the cross-sectional triangle (Δ MNO) remains completely identical (congruent) to the base triangles (Δ ABC and Δ A'B'C') no matter where you cut it.
Interaction Guide:
• Use the slider to slide the cut.
• Click/Touch & Drag directly on the canvas to rotate the prism in 3D.
Current State:
• Base Face: Δ ABC
• Slice Face: Δ MNO
• End Face: Δ A'B'C'
Therefore: Δ ABC ≅ Δ MNO ≅ Δ A'B'C'

Characteristics of Prism

  1. It has two parallel congruent opposite polygons, called the base of the prism. The prism of the base triangle is a triangular prism and the prism of the base rectangle is a rectangular prism.
  2. The surface parallel with the base in a prism is called the cross-section of the prism. This cross-section is congruent with the base.
  3. Generally there are two types of prism called oblique and right. In this class, we discussed on right prism only (all the faces except the base are perpendicular to the base).
  4. The areas of all faces other than their bases in the prism is called the lateral surface area of the prism.
  5. The perpendicular distance between two bases is the height or length of the prism.
  6. The volume of the prism (V) = Area of the base (A) × height (h)

Area of the bases in a triangular prism

(a) Area of the equilateral triangle
A = √34 × a2
(b) Area of the isosceles triangle
A = b4 × √(4a2 − b2)
(c) Area of the scalene triangle
A = √(s(s−a)(s−b)(s−c))
where, s = a + b + c2
(d) Area of right angled triangle
A = 12 × p × b
(e) Area of right angle isosceles triangle
A = 12 p2  or,  12 b2
(f) Area of the base in a rectangular prism
A = l × b
(g) Area of the base in square prism
A = l2
Solve Questions — Cross-Section Area of Prism
Equilateral: A = √34a²  |  Isosceles: A = b4√(4a²−b²)
Right △: A = 12×p×b  |  Right Isosc.: A = 12p²
Rectangle: A = l×b  |  Square: A = l²