Question

The base of an isosceles triangle is 12 cm and its perimeter is 32 cm. Find its area.
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Answer 1

Answer:

48 cm square........................

Answer 2

Step-by-step explanation:

$☣ \large\rm \bf{Given}$

Perimeter of an isosceles triangle = 32cm

Base of an isosceles triangle = 12cm

$☣ \large \rm\bf{Find}$

Area of the triangle

$☣ \large \rm\bf{Explanation}$

Perimeter of an isosceles traingle = 2a + b

32 = 2a + 12

⤍ 2a = 32 - 12

⤍ 2a = 20

⤍ a = $\frac{20}{2}$

a = 10cm

To find the area we need to find the height

Let us divide the triangle into two equal parts

Hypotenuse² = Base² - height²

Hypotenuse = 10cm

Base = $\frac{12}{2}$ = 6cm

Height² = Hypotenuse² - Base²

Height² = 10² - 6²

Height² = 100 - 36

Height² = √64

Height = 8cm

$\small\bf Area \: of \: a \: triangle = \frac{1}{2} \times base \times height$

$\small\rm{ Area \: of \: a \: triangle = \frac{1}{2} \times 12 \times 8 }$

$\small\rm{ Area \: of \: a \: triangle = \frac{1}{2} \times 96 }$

$\small\rm{ Area \: of \: a \: triangle =48 }$

Area of a triangle = 48cm²