Question

The height of an equilateral triangle measures 9 cm . Find its area, correct to 2 places
of decimals

Answer 1

6.022 is correct answer

Answer 2

height of equilateral triangle=

$\sqrt{3} \div 2 \times a$

then

$\sqrt{3} \div 2 \times a = 9$

then

$a = 9 \times 2 \div \sqrt{3}$

$a = 18 \div \sqrt{3}$

$a = 6 \sqrt{3}$

and

as we know that

area of equilateral triangle =

$\sqrt{3} \times {a}^{2} \div 4$

then

$\sqrt{3} \times( 6 \sqrt{3 } )^{2} \div 4$

$\sqrt{3} \times 36 \times 3 \div 4$

$\sqrt{3} \times 9 \times 3$

$27 \sqrt{3}$

=27×1.73

=46.71cm^2