Question

find the area of these triangles using correct formulae ​

Answer 1

★ Concept:-

Here in this question, concept of Pythagoras theorem is used

We are given a triangle whose hypotenuse and height are given and we are asked to find its area. To find its area it is necessary to find height of triangle so that we can apply formula for area of triangle.

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★ Given:-

• Hypotenuse=25cm²

• Height=9cm

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★ To find:-

• Area of triangle

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★ Solution:-

Applying Pythagoras theorem in the given triangle:

Hypotenuse²=Base²+Perpendicular²

⇒ (25cm)²=Base²+(9cm)²

⇒ 625cm²=Base²+81cm²

⇒ 625cm²-81cm²=base²

⇒ 544cm²=Base²

⇒ √544cm²=Base

⇒ 23.3cm=Base

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Now applying formula for area:

Area of Triangle=½×Base×Height

Area of triangle=½×23.3cm×9cm

Area of triangle=104.85cm²

So the required area of triangle is 104.85cm².

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Answer 2

Length of the another side = √ 25² - 9²

= √ 625 - 81

= √ 544 unit

Area of triangle = ½bh = ½(9)(√544)

= ½ 9 (4 √34)

= 18 √34 = 104.957 unit ²

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