A triangular pyramid is a geometric shape that has a triangular base and three triangular faces. It has a vertex, common to all the three lateral faces of a triangular pyramid. If all the three triangular faces are equilateral, then such a pyramid is called a tetrahedron. Show
A Pyramid is a polyhedron that has a base and three or more than three triangular faces that meeting at a point above the base (the apex). Triangular pyramids are formed solely from triangles. The 3 triangular sides slant upwards to form the triangular base. As it is formed from four triangles, a triangular-based pyramid is also called a tetrahedron. Learn more about pyramids here. The base of the pyramid could be based on different types of triangles. If all the faces are equilateral triangles or triangles whose edges are all equal lengths, the pyramid is called a regular tetrahedron. If the triangles have edges of various lengths, the pyramid is an irregular tetrahedron. A triangular pyramid is a pyramid which has a triangular base. In geometry, vertices are essentially corners. All triangular-based pyramids, either regular or irregular, have four vertices. Triangular-based pyramids have 6 edges, 3 are along the base and 3 are extending up from the base. If the six edges are of the same length, all the triangles are equilateral, and the pyramid is called a regular tetrahedron. Types of Triangular PyramidsThe different types of triangular pyramids are :
Regular Triangular PyramidA pyramid has a base with sides that are equal in length. For the triangular pyramid, the base of regular tetrahedron should be an equilateral triangle. Non-Regular Triangular PyramidA pyramid has a base with sides that have different lengths. The base of the triangular pyramid has unequal sides. Or we can say, the base could be a scalene triangle or an isosceles triangle. Right Triangular PyramidA three-Dimensional shape with a right-angle triangle at its base extruding up to a single point is a right-triangular pyramid. Properties of Triangular Pyramid
Triangular Pyramid FormulaThe formula for the area and volume of the triangular pyramid is given here. We can use these formulas to solve the problems based on them. Volume of Triangular PyramidTo find the volume of a triangular-based pyramid, multiply the area of the triangular base and the height of the pyramid (measured from the base to the apex). Then, divide this number by three. Volume = ⅓ × Base Area × Height Surface Area of Triangular PyramidTo determine the surface area of a triangular-based pyramid, add together the area of the base and the area of all the sides. For regular tetrahedra, this calculation is simple. Find the length of the base and the height of one of the triangles. Multiply those measurements collectively and divide this number by two. This is the area of one of the triangles. Now, multiply this area by four to account for all the triangular faces of the pyramid. For irregular tetrahedra, find the area of every triangle individually, using the area formula. Then, add all the areas together. Surface Area = (Base area) + ½ × Perimeter × (Slant length) Net of a Triangular PyramidA net of the triangular pyramid is the pattern formed when the surface of it is laid out flat showing each triangular face of the figure. For different types of solids, the net pattern is different. To find the net of a solid we should keep a note of the following points:
Note: Nets are helpful when we need to find the surface area of the solids. Triangular Pyramid Solved ExamplesExample 1: Find the surface area of a triangular pyramid with the base area is 28cm.sq., the perimeter is 20cm, slant length is 5cm. Solution: Surface area = [Base area] + ½ × Perimeter × [Slant length] = 28 + ½ × 20 × 5 = 28 + 50 = 78 cm.sq. Example 2: Find the volume of a triangular pyramid with a base area is 28cm, height is 4.5cm. Solution: Volume = ⅓ × Base Area × Height = ⅓ × 28 × 4.5 = ⅓ × 126 = 42 cubic.cm. Example 3: Find the volume of the following triangular pyramid, rounding your answer to two decimal places. Solution: V = ⅓ × AH = ⅓ × (½ bh) H = ⅙ bhH = ⅙ × 19 × 17 × 23 = 1238.17 (Correct to 2 decimal places) So, the volume is 1238.17 cm3 Practise Questions
Frequently Asked Questions – FAQsA triangular pyramid is a geometric shape that has a triangular base and three triangular faces, having a common vertex. A triangular pyramid has four faces, one in the base and three lateral faces. A triangular pyramid has four
vertices. One vertex is common to all three faces of the pyramid. There are three types of triangular pyramids. They are regular, irregular, and right-angled triangular pyramids. How many faces edges and vertices a triangular pyramid has *?Triangular pyramid has 4 faces, edges and vertices.
How many edges do triangular pyramid have?Triangular-based pyramids have 6 edges, 3 are along the base and 3 are extending up from the base. If the six edges are of the same length, all the triangles are equilateral, and the pyramid is called a regular tetrahedron.
How many edges faces and vertices does a triangular prism have?A triangular prism is polyhedron and a three-dimensional shape that has 5 faces, 6 edges and 9 vertices. Its bases are triangular and sides are rectangular.
How many number of faces does a triangular pyramid have?4Tetrahedron / Number of facesnull
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