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Mathematics

Assertion (A) : The area of an equilateral triangle of height 23 is 432\sqrt{3} \text{ is } 4\sqrt{3} cm2.

Reason (R) : The area of an equilateral triangle = 13\dfrac{1}{\sqrt{3}} x (Height)2.

  1. Both A and R are correct, and R is the correct explanation for A.

  2. Both A and R are correct, and R is not the correct explanation for A.

  3. A is true, but R is false.

  4. A is false, but R is true.

Area Trapezium Polygon

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Answer

Given, height of the equilateral triangle = 2 3\sqrt{3} cm

By formula,

The area of an equilateral triangle = 13\dfrac{1}{\sqrt{3}} x (Height)2

So, reason (R) is true.

Substituting values we get :

Area=13×(23)2=13×4×3=43 cm2.\text{Area} = \dfrac{1}{\sqrt{3}} \times (2\sqrt{3})^2 \\[1em] = \dfrac{1}{\sqrt{3}} \times 4 \times 3 \\[1em] = 4\sqrt{3} \text{ cm}^2.

So, assertion (A) is true.

∴ Both A and R are correct, and R is the correct explanation for A.

Hence, option 1 is the correct option.

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