Chapter 11: Q12. (page 431)

Find the area of each figure:
An equilateral triangle with perimeter.18

Short Answer

Expert verified

The area of given figure is $9 \sqrt{3}$ square units.

Step by step solution

Step 1. Analyze the given information.

Let the common sides be x

We know that in equilateral triangle all three sides are equal in length.

The perimeter of equilateral triangle18, which means the sum of all three sides will be equal to 18

$x + x + x = 18$

$3 x = 18$

$x = 6$

Thus, the sides of triangle are

$6, 6, 6$

Step 2. Concept used.

Area of an equilateral triangle can be found using the formula

$A = \frac{\sqrt{3}}{4} a^{2}$

Where,

a=The sides of triangle.

Step 3. Find the area of given figure.

$A = \frac{\sqrt{3}}{4} a^{2}$

$= \frac{\sqrt{3}}{4} {(6)}^{2}$

$= \sqrt{3} \times 3 \times 3$

$= 9 \sqrt{3}$ Square units.

Therefore, the area of given figure is $9 \sqrt{3}$ square units.

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Find the area of each figure:
An equilateral triangle with perimeter.18

Short Answer

Step by step solution

Step 1. Analyze the given information.

Step 2. Concept used.

Step 3. Find the area of given figure.

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Find the area of each figure:An equilateral triangle with perimeter.18

Short Answer

Step by step solution

Step 1. Analyze the given information.

Step 2. Concept used.

Step 3. Find the area of given figure.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Logic and Functions

Statistics

Geometry

Theoretical and Mathematical Physics

Calculus

Study anywhere. Anytime. Across all devices.

Find the area of each figure:
An equilateral triangle with perimeter.18