Question

If the base of a right-angled triangle is 6 cm and the hypotenuse is 10 cm, find its area.
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Answer 1

QuestioN:-

• If the base of a right-angled triangle is 6 cm and the hypotenuse is 10 cm, find its area.

AnsweR: Area of triangle is 24 cm²

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Step by step explanation:-

Given :-

• Base of triangle is 6 cm
• Hypotenuse of triangle is 10cm

To find :- Area of triangle

Concept:-

• First we have to find height of triangle means perpendicular by using Pythagoras theorem
• Then we use Formula of area because we need area of triangle according to question.

SolutioN:-

We know that Pythagoras theorem is

◆(Perpendicular)² + (base)² = ( Hypotenuse)²

• Now substitute the values in this formula.

➟ (Perpendicular)² + (6)² = (10)²

➟ (Perpendicular)² + 36 = 100

➟ (Perpendicular)² = 100 - 36

➟ (Perpendicular)² = 64

➟ Perpendicular = √64

➟ Perpendicular = 8 cm

As we all know perpendicular is also known as height.

Then , we want the area of triangle, So formula for area is :-

◆Area = 1/2 × base × height

Put the values of base = 6 cm and height = 10 cm for area

⇝ Area = 1/2 × 6 × 8

⇝ Area = 6 × 4

⇝ Area = 24 cm²

Answer 2

Answer

• Area of triangle = 24 cm²

Given

• The base of a right-angled triangle is 6 cm and the hypotenuse is 10 cm

To Find

• Area of the right triangle

Formula Used

• Pythagoras Theorem
• (Opp.)² + (Adj.)² = (Hyp.)²
• Area of the triangle
• ¹/₂ × Base × Height

Solution

Find attachment .

Apply Pythagoras theorem for finding height , x .

⇒ x² + 6² = 10²

⇒ x² + 36 = 100

⇒ x² = 100 - 36

⇒ x² = 64

⇒ x = 8 cm

So , height  , x = 8 cm

Now , Apply area of triangle .

⇒ ¹/₂ × Base × Height

⇒ ¹/₂ × 6 × 8

⇒ 3 × 8

⇒ 24 cm²

So , Area of triangle is 24 cm²  ←