Question

If the perimeter of an equilateral triangle is 36 cm , calculate its area and height.
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Answer 1

Step-by-step explanation:

perimeter = 3a where a is the side of equilateral triangle.

36cm = 3a

side =12 cm

area =√3÷4 a2 = √3÷4×144.

√336cm2

area of triangle = 1÷2 base × height .

36√3= 6cm× height .

height= 36√3÷6= 6√3= 1.732× 6.

10.4 cm

Answer 2

GIVEN :

• PERIMETER OF EQUILATERAL TRIANGLE IS 36 cm

TO FIND :

• AREA AND HEIGHT OF THE EQUILATERAL TRIANGLE

SOLUTION :

PERIMETER OF EQUILATERAL TRIANGLE = 36 cm

$3a = 36 \\ \\ = > a = 12 \: cm$

AREA OF EQUILATERAL TRIANGLE = √3a² / 4

$= \frac{ \sqrt{3} \times 12 \times 12 }{4} \\ \\ = 36 \sqrt{3} \: \: cm {}^{2}$

HEIGHT OF AN EQUILATERAL TRIANGLE = √3a / 2

$= \frac{ \sqrt{3} \times 12 }{2} = 6 \sqrt{3}$

FORMULAS USED :

$i) \: area \: of \: equilateral \: tringle = \frac{ \sqrt{3} {a}^{2} }{4} \\ \\ ii) \: height \: of \: equilateral \: triangle = \frac{ \sqrt{3}a }{2} \\ \\ iii) \: perimeter \: of \: equilateral \: triangle = 3a$

∴ AREA , HEIGHT OF THE EQUILATERAL TRIANGLE ARE 36√3 cm² AND 6√3 cm

HOPE IT HELPS !!!!