Question

The area of triangle is half of a parallelogram standing the same basee two parallel line the three sides of the triangle are 15cm, 12cm, 9cm. Find the area of the parallelogram. If the base is 12cm. Find its length

Answer 1

the height of the parallelogram 9 cm.

Explanation:

Let's start by finding the area of the triangle using Heron's formula, which does not require the triangle to be right-angled:

Given sides of the triangle: a = 15 cm, b = 12 cm, c = 9 cm.

Semi-perimeter (s) of the triangle = (a + b + c) / 2 = (15 + 12 + 9) / 2 = 36 / 2 = 18 cm.

Now, using Heron's formula, the area (A) of the triangle is given by:

A = √(s * (s - a) * (s - b) * (s - c))

A = √(18 * (18 - 15) * (18 - 12) * (18 - 9))

A = √(18 * 3 * 6 * 9)

A = √(2916)

A ≈ 54 cm²

Now, since the area of the triangle is half of the parallelogram with the same base, the area of the parallelogram can be found by simply doubling the area of the triangle:

Area of parallelogram = 2 * Area of triangle

Area of parallelogram = 2 * 54 cm²

Area of parallelogram = 108 cm²

Now, we are given the base of the parallelogram as 12 cm. Let's find its height (h) using the formula for the area of a parallelogram:

Area of parallelogram = base * height

108 cm² = 12 cm * height

To find the height (h), divide both sides by 12 cm:

height (h) = 108 cm² / 12 cm

height (h) = 9 cm

Therefore, the length of the parallelogram (height) is 9 cm.Let's start by finding the area of the triangle using Heron's formula, which does not require the triangle to be right-angled:

Given sides of the triangle: a = 15 cm, b = 12 cm, c = 9 cm.

Semi-perimeter (s) of the triangle = (a + b + c) / 2 = (15 + 12 + 9) / 2 = 36 / 2 = 18 cm.

Now, using Heron's formula, the area (A) of the triangle is given by:

A = √(s * (s - a) * (s - b) * (s - c))

A = √(18 * (18 - 15) * (18 - 12) * (18 - 9))

A = √(18 * 3 * 6 * 9)

A = √(2916)

A ≈ 54 cm²

Now, since the area of the triangle is half of the parallelogram with the same base, the area of the parallelogram can be found by simply doubling the area of the triangle:

Area of parallelogram = 2 * Area of triangle

Area of parallelogram = 2 * 54 cm²

Area of parallelogram = 108 cm²

Now, we are given the base of the parallelogram as 12 cm. Let's find its height (h) using the formula for the area of a parallelogram:

Area of parallelogram = base * height

108 cm² = 12 cm * height

To find the height (h), divide both sides by 12 cm:

height (h) = 108 cm² / 12 cm

height (h) = 9 cm

Therefore, the length of the parallelogram (height) is 9 cm.