Question

find the area of triangle
() whose height is 6 cm and base
is 10 cm.
(1) whose three sides are 17 cm, 8 cm and 15 cm long.
Find the area of a triangle :
Also, in part (ii) of this question; calculate the length of the altitude corresponding
to the largest side of the triangle.​

Answer 1

Step-by-step explanation:

(i) ✤ Height = 6 cm.

✤ Base = 10 cm.

☘ Area of triangle = 1/2 × base × height

= 1/2 × 6 × 10

= 60/2

= 30

Thus,

Area of triangle is 30 cm².

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(ii) ✤ Sides of triangle are 17 cm, 8 cm and 15 cm.

Here, we will use Heron's formula for finding area because height is not given.

Formula for heron's formula is:

Area of triangle = √s(s - a)(s - b)(s - c)

Where,

• s is semi-perimeter of triangle.
• a, b and c are sides of triangle.

So,

Semi-perimeter = Perimeter/2

Semi-perimeter = 17 + 8 + 15/2

Semi-perimeter = 40/2

Semi-perimeter = 20

Semi-perimeter of triangle is 20 cm.

Area of triangle :

$\longrightarrow$ √20×(20 - 17)(20 - 8)(20 - 15)

$\longrightarrow$ √20 × 3 × 12 × 5

$\longrightarrow$ √2×2×5×3×2×2×3×5

$\longrightarrow$ 2×5×3×2

$\longrightarrow$ 60

Thus,

Area of triangle is 60 cm².

17 is largest side of triangle.

Now,

If we see triangle taking base 17 cm. Then, Area of triangle will be same.

Let, the altitude corresponding to the base 17 cm be h.

So,

$\longrightarrow$ 60 = 1/2 × 17 × h

$\longrightarrow$ 60 × 2 = 17 × h

$\longrightarrow$ 120 = 17 × h

$\longrightarrow$ 120/17 = h

$\longrightarrow$ h = 7.05

Therefore,

Altitude corresponding to the largest side is 7.05 cm.

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Diagrams of both questions are in attachment

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Answer 2

Answer:

(i) Height = 6 cm.

Base = 10 cm.

Area of triangle = 1/2 × base × height

= 1/2 × 6 × 10

= 60/2

= 30

(ii) Sides of triangle are 17 cm, 8 cm and 15 cm.

Here, we will use Heron's formula for finding area because height is not given.

Formula for heron's formula is:

Area of triangle = √s(s - a)(s - b)(s - c)

Where,

s is semi-perimeter of triangle.

a, b and c are sides of triangle.

So,

Semi-perimeter = Perimeter/2

Semi-perimeter = 17 + 8 + 15/2

Semi-perimeter = 40/2

Semi-perimeter = 20

Semi-perimeter of triangle is 20 cm.

Area of triangle :

⟶ √20×(20 - 17)(20 - 8)(20 - 15)

⟶ √20 × 3 × 12 × 5

⟶ √2×2×5×3×2×2×3×5

⟶ 2×5×3×2

⟶ 60

Thus,

Area of triangle is 60 cm².

17 is largest side of triangle.

Now,

If we see triangle taking base 17 cm. Then, Area of triangle will be same.

Let, the altitude corresponding to the base 17 cm be h.

So,

⟶ 60 = 1/2 × 17 × h

⟶ 60 × 2 = 17 × h

⟶ 120 = 17 × h

⟶ 120/17 = h

⟶ h = 7.05

Therefore,

Altitude corresponding to the largest side is 7.05 cm.