Question

The base of a right angle triangle measures 4 cm and its hypotenuse measure 5 cm . Find the area of the triangle.​

Answer 1

Answer :

›»› The area of a right angle triangle is 6 cm².

Given :

• The base of a right angle triangle measures 4 cm and its hypotenuse measure 5 cm.

To Find :

• The area of the right angle triangle.

How to solve?

Here in this question we have to find the area of right angle triangle. So, firstly we need to find the height of right angle triangle, after that we will find the area of the right angle triangle on the basis of conditions given above.

Since, we are provided with two elements that used in formula, hypotenuse and base of a right angle triangle, by using Pythagoras theorem we find the height of the right angle triangle$.$

To find the area of triangle, we use the formula for finding the area which says Area of triangle = ½ × base × height.

Solution :

Let us assume that, the height of a right angle triangle is x cm.

To find the height of the right angle triangle, we use the formula:-

❰ Hypotenuse² = Perpendicular² + Base² ❱

• Hypotenuse = 5 cm.
• Perpendicular = Height = x = ?
• Base = 4 cm.

According to the given question,

On putting the given values in the formula, we get

⇛ 5² = x² + 4²

⇛ 25 = x² + 4²

⇛ 25 = x² + 16

⇛ x² = 25 - 16

⇛ x² = 9

⇛ x = √9

⇛ x = 3

Now, we have two elements that used in formula, Base and height of a right angle triangle.

To find the area of right angle triangle, we use the formula:-

❰ Area of triangle = ½ × base × height ❱

• Base = 4 cm.
• Height = 3 cm.

According to the given question,

On putting the given values in the formula, we get

⇛ Area of triangle = ½ × 4 × 3

⇛ Area of triangle = 1 × 2 × 3

⇛ Area of triangle = 2 × 3

⇛ Area of triangle = 6

Hence, the area of a right angle triangle is 6 cm².

Answer 2

Answer:

Given :-

• The base of a right angle triangle measures 4 cm and its hypotenuse measure is 5 cm.

To Find :-

• What is the area of the triangle.

Formula Used :-

⓵ Phythagorus Theorem,

$\boxed{\bold{\small{h²\: =\: b²\: +\: p²}}}$

where,

• h = Hypotenuse
• b = Base
• p = Perpendicular

⓶ Area of the triangle,

$\boxed{\bold{\small{Area\: of\: the\: triangle\: =\: \dfrac{1}{2} ×\: base\: ×\: height}}}$

Solution :-

⓵ Given :

• Base = 4 cm
• Hypotenuse = 5 cm

In right triangle, the height is the third side apart from base and hypotenuse.

So, by using the Phythagorus Theorem we know that,

✦ h² = b² + p²

⇒ (5)² = (4)² + p²

⇒ 25 = 16 + p²

⇒ p² = 16 - 25

⇒ p² = 9

⇒ p = $\sqrt{9}$

➠ p = 3 cm

So, the perpendicular (height) = 3 cm

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⓶ Now, we have to find the area of the right angle triangle we know that,

✦ Area of the triangle = $\dfrac{1}{2}$ × base × height

⇒ Area of the triangle = $\dfrac{1}{2}$ × 4 × 3

⇒ Area of the triangle = $\dfrac{1}{2}$ × 12

➥ Area of the triangle = 6 cm²

$\therefore$ The area of the triangle is 6 cm² .

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