Question

Find the area of an isosceles triangle whose base is 6 cm and perimeter is 16 cm​

Answer 1

Answer:

see the given attachment

Answer 2

Given:

• Perimeter of an Isosceles triangle = 16 cm
• Base of Isosceles triangle = 6 cm

To find:

• Area of an Isosceles triangle?

Solution:

Let ABC be an Isosceles triangle.

Let two equal sides of an Isosceles triangle be x cm.

Perimeter of ∆ABC = 16 cm

⇏ AB + AC + BC = 16 cm

⇏x + x + 6 = 16

⇏2x + 6 = 16

⇏ 2x = 16 - 6

⇏ 2x = 10

⇏ x = 5 cm

⇏ AB = BC = 5 cm

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Method 1:

Now, let AD be the perpendicular median of ∆ ABC,

Therefore,

• BD = DC = BC/2 = 6/2 = 3 cm

• AC = 5 cm

Now, Using Pythagoras Theorem in ∆ ADC,

⇏ AC² = DC² + AD²

⇏ 5² = 3² + AD²

⇏ AD² = 5² - 3²

⇏ AD² = 25 - 9

⇏ AD² = 16

⇏√AD² = √16

⇏ AD = 4 cm

Now, Finding Area of ∆ ABC,

Area = 1/2 × Base × Height

⇏ 1/2 × 6 × 4

⇏ 6 × 2

⇏ 12 cm²

∴ Hence, Area of ∆ABC is 12 cm².

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Method: 2

Perimeter of ∆ABC = 16 cm

Semi - perimeter of ∆ ABC , s = 16/2 = 8 cm

Here,

• BC = 6 cm
• AB = 5 cm
• AC = 5 cm

Therefore,

Using Heron's Formula,

Area = √s(s - a)(s - b)(s - c)

⇏ √8(8 - 6)(8 - 5)(8 - 5)

⇏ √8 × 2 × 3 × 3

⇏ √144

⇏ 12 cm²

∴ Hence, Area of ∆ABC is 12 cm².