How To Find Base Area Of Triangular Prism

Base Area of a Triangular Prism

In this section, we volition talk over the base area of a triangular prism forth with solved examples. The base area of a triangular prism is the area of the triangle of the prism. Let u.s.a. start with the pre-required cognition to empathize the topic base expanse of a triangular prism. Recall that a prism is a solid which has identical polygon ends (bases), flat parallelogram sides, and has the same cross-department all along its length.

A prism having iii faces as rectangles and ii triangles every bit its bases (one triangle acts as the top) is called a triangular prism. It's a 3-sided prism where the base and top are equal triangles and the remaining three sides are rectangles. Both of the triangles are parallel and congruent to each other. The rectangles need not be coinciding with each other.

1.	What Is Base of operations Area of a Triangular Prism?
2.	Base Area of a Triangular Prism Using Sides
3.	Base Surface area of a Triangular Prism Formula with Height and Base
4.	FAQs on Base Area of Triangular Prism

What Is Base Expanse of a Triangular Prism?

The base of operations expanse of a triangular prism is defined as the full area covered by the bases of a triangular prism. The base area of the triangular prism is expressed in foursquare units. The expanse of the base of a triangular prism can be calculated using unlike formulas, depending upon the known parameters and type of triangle in the base. Let usa empathize these formulas in the following sections.

Base Expanse of a Triangular Prism if the Sides of Its Triangle Are Given

For a triangular prism, if the length of the sides of the triangular base of the prism is given, then its base area tin be given by:
Base area of a triangular prism = Area of the base triangle

Using Heron's formula for the area of a triangle nosotros get,
Base area of a triangular prism = √[southward(s − a)(south − b)(southward − c)]
where,

a, b, c are the lengths of the sides of the base triangle, and,
s is its semi-perimeter and is equal to (a + b + c)/ii

base area of triangular prism

Example: How to detect the base area of a triangular prism given the length of the sides of the base triangle: a = 20 units, b = 10 units, and c = 20 units?

Semi-perimeter (due south) = (20 + 10 + 20)/ii = 25 units

Base area of the given triangular prism = √[due south(due south − a)(s − b)(south − c)] = √[25(25 − 20)(25 − 10)(25 − 20)] = √[25(5)(15)(5)] = 25√fifteen square units.

Base Area of a Triangular Prism Formula if the Base and Meridian of the Triangle Are Given

For a triangular prism, if the length of the base and summit of the base of operations triangle is given, then its base area can be given by,

Base of operations area of a triangular prism = Expanse of the base triangle

Base of operations surface area of a triangular prism = (1/two) × b × h

where,

b is the length of the base of the triangle, and,
h is the height of the triangle

base area of triangular prism

Instance: How to observe the base surface area of a triangular prism given the height of the triangle h = 10 units and base of operations b = twenty units?

Solution: Base area of the given triangular prism = (1/2) × b × h = (ane/2) × 20 × 10 = 100 square units

Important Notes on Base Area of a Triangular Prism

The base of operations area of a triangular prism can be calculated when iii sides of the base triangle are given.
The base of operations area of a triangular prism tin be calculated when the base of operations length and peak of the base triangle are given.

Related Topics on Base of operations Area of a Triangular Prism

Triangular Prism
Volume of Foursquare Prism
Surface Expanse of Prism

Solved Examples on Base of operations Area of a Triangular Prism

Example 1: Discover the base surface area of the triangular prism whose base triangle has the summit = sixty units and base length = 40 units.

Solution:

Height of the triangular prism = 60 units

Base length of the triangular prism = 40 units

Base of operations area of the given triangular prism = 1/two × Base length × Height of the base triangle = 1/2 × lx × 40 = 120 square units

Reply: Base area of the given triangular prism = 120 foursquare units
Example 2: Find the base surface area of the triangular prism whose base triangle has the length of the sides a= iii units, b = four units, and c = 5 units.

Solution:

Length of the sides a= iii units, b = 4 units, and c = 5 units.

Semi-perimeter of the base triangle (s) = (3 + 4 + 5)/2 = 6 units

Base area of the given triangular prism = √[southward(s−a)(s−b)(s−c)]s = √[half-dozen(half dozen−3)(vi−4)(6−5)] = √[6(3)(ii)(1)] = 6 square units

Respond: Base area of the given triangular prism = 6 square units.

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Practice Questions on Base of operations Area of a Triangular Prism

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FAQs on the Base Area of a Triangular Prism

What Is Base of operations Area Triangular Prism?

The base area of a triangular prism is defined as the region or area covered by the bases of a triangular prism. A triangular prism has ii triangle-shaped bases.

How to Calculate the Base of operations Area of a Triangular Prism?

The base area of a triangular prism can be calculated as,

Note down the dimensions of the triangle in bases.
Apply the formulas to calculate the surface area of the base triangle and multiply it by 2.
Express the issue with a suitable unit.

What Are the Formulas to Find Base of operations Surface area of a Triangular Prism?

The formulas that tin can exist used to find the base area of a triangular prism are,

When base triangle is equilateral, with each side 'a', then area = √3a²/4.
When base triangle's base 'b' and height 'h' is given, then surface area = (1/two) bh.
When base triangle is a right-angled triangle, with two legs 'b' and 'h' and then expanse = (ane/2) bh.
When base triangle is an isosceles triangle with its sides to be 'a', 'a', and 'b' then its surface area is (b/iv) · √(4a² - b²)
When base of operations triangle is scalene, with all three sides 'a', 'b', and 'c' are given, and then area = √[s(s - a)(due south - b)(southward - c)], where s = (a + b + c)/2.
When base triangle's 2 sides 'a' and 'b' and the included bending 'θ' are given, and then area = 1/2 ab sin θ.

What Are the Units Used to Express Base Expanse of a Triangular Prism?

The units used to express the base of operations surface area of a triangular prism are inⁱⁱ, m², cm², ft^two, etc. It is expressed in foursquare units.

How to Calculate the Base Length Using Base of operations Area of a Triangular Prism?

Using the area of triangle formula for the given type of triangle in base, we tin can calculate the base length by substituting the known values in the formula and solve.