Question

Find the area of an isosceles triangle with two equal sides 2 cm and an unequal side of length 3 cm

Answer 1

if we drop a perpendicular on its base {unequal side} then it bisects the side and it will become 3/2cm
now we can find the height{perpendicular} by Pythagoras theorem
${2}^{2} = {h}^{2} + {( \frac{3}{2}) }^{2}$

${h}^{2} = 4 - { \frac{9}{4} }$
${h}^{2} = \frac{7}{4}$
$h = \frac{ \sqrt{7} }{2}$
$area = \frac{1}{2} \times base \times height$
$area = \frac{1}{2} \times 3 \times \frac{ \sqrt{7} }{2}$
$= \frac{ 3\sqrt{7} }{4} {cm}^{2}$

Answer 2

Since an isosceles triangle has two equal sides, if the triangle is split in half vertically, the length of the base on each side is:

3cm÷2=1.5cm

We can then use the Pythagorean theorem to find the height of the triangle.

The formula for the Pythagorean theorem is:

a2+b2=c2

To solve for the height, substitute your known values into the equation and solve for a:

where:
a = height
b = base
c = hypotenuse

a²+b²=c²
a²=c²−b²
a2=(2)²−(1.5)²
a2=(4)−(2.25)
a2=1.75
a=√1.75
a=1.32

Now that we have our known values, substitute the following into the formula for area of a triangle:

base=3cm
height=1.32cm

Area=base⋅height2

Area=(3)⋅(1.32)2

Area=3*2904/10000

Area=0.8712

∴the area is 0.8712 cm².