A triangle with sides 12, 16 and 20 units is given.

Statement 1: To find the area of this triangle, the formula " $A r e a = \frac{1}{2} \times b a s e \times h e i g h t$ " is the ideal one to be used.

Statement 2: To find the area, the formula " $A r e a = \sqrt{s (s - a) (s - b) (s - c)}$ " is the ideal one to be used.

Enter “1” if you feel Statement 1 is correct, or “2” if Statement 2 is correct.
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Solution

Observe that $12^{2} + 16^{2} = 144 + 256 = 400 = 20^{2}$ , i.e., this triangle is right angled, with 20 units as the hypotenuse and the other two sides forming the base and the height.
So,
$A r e a = \frac{1}{2} \times b a s e \times h e i g h t$
is the ideal one to proceed.

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Similar questions

Assertion: Area of a triangle
$= \sqrt{s (s - a) (s - b) (s - c)}$ where a, b and c are the sides of the triangle and $s = \frac{a + b + c}{2}$

Reason: Area of a triangle $= \frac{1}{2} \times b a s e \times h e i g h t$
Which of the following is correct?

Q. The Heron's formula to find the area of a triangle is

\sqrt{s (s - a) (s - b) (s - c)}

Consider the following two statements

Statements - 1: The area of a right angled triangle
$= \frac{Product of the two sides containing right angle}{2}$

Statement - 2: If the perimeter of a triangle is s and the sides of the triangle are a, b and c respectively then the area of the triangle
$= \sqrt{s (s - a) (s - b) (s - c)}$

Which of the following is true?

The formula to find the area of a triangle: $\frac{1}{2} \times$ base $\times$ height, is valid only for a right angled triangle.

Q. Heron's formula for finding area of a triangle is:

\sqrt{s (s - a) (s - b) (s - c)}

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Observe that 122+162=144+256=400=202, i.e., this triangle is right angled, with 20 units as the hypotenuse and the other two sides forming the base and the height. So, Area=12×base×height is the ideal one to proceed.

Observe that $12^{2} + 16^{2} = 144 + 256 = 400 = 20^{2}$ , i.e., this triangle is right angled, with 20 units as the hypotenuse and the other two sides forming the base and the height.
So,
$A r e a = \frac{1}{2} \times b a s e \times h e i g h t$
is the ideal one to proceed.