Question

if the base of a right - angled triangle is 12 cm and hypotenuse 13 cm , the its area is
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Answer 1

$\huge\mathfrak\red{Answer}$

Given :-

Base of triangle = 12cm

Hypotenuse of triangle = 13cm

To Find :-

Height of triangle

Area of Right- angled triangle

Solution :-

Consider the ∆ABC

So, AC = 13cm

BC = 13cm

By Using Pythagoras theorem :-

$AC² = AB² + BC²$

$AB = \sqrt{13 {}^{2} - {12}^{2} }$

$AB = 5cm$

Hence, Height of triangle is 5cm

Area of ∆ABC =

$\frac{1}{2} \times base \times height$

$\frac{1}{2} \times 12 \times 5$

$30cm^{2}$

Hence the area of right- angled triangle is 30cm²

Answer 2

Given :-

Base of triangle = 12cm

Hypotenuse of triangle = 13cm

To Find :-

Height of triangle

Area of Right- angled triangle

Solution :-

Consider the ∆ABC

So, AC = 13cm

BC = 13cm

By Using Pythagoras theorem :-

AC² = AB² + BC²AC²=AB²+BC²

AB = \sqrt{13 {}^{2} - {12}^{2} }AB=

13

2

−12

2

AB = 5cmAB=5cm

Hence, Height of triangle is 5cm

Area of ∆ABC =

\frac{1}{2} \times base \times height

2

1

×base×height

\frac{1}{2} \times 12 \times 5

2

1

×12×5

30cm^{2}30cm

2

Hence the area of right- angled triangle is 30cm²