Question

A field is in the form of a triangle. If its area is 3.5 ha and the length of its base is 350 m
then find its altitude​

Answer 1

⇒ Given:

A field is in the form of a triangle.

Area of the field is 3.5 ha.

Length of its base is 350 m.

⇒  To Find:

The length of the altitude of the field.

⇒ Analysis:

At first, we need to convert hectares to meters. This can be done by using the conversion formula. Then, we can use the formula to find the area of the triangle and find the altitude by applying the values that we know.

⇒ Formulae to be used:

→ $\boxed{\sf{1\:hectare=10000\:m}}$

→ $\boxed{\sf{Area\:of\:a\:triangle=\dfrac{1}{2}bh}}$

⇒ Solution:

First, we can convert 3.5 ha to meters.

We know that:

1 ha = 10000 m

So,

3.5 ha = 3.5 x 10000

= 35000 m²

Area of a triangle = 1/2 x base x height ------ (1)

Area of the given triangle = 35000 m² ------ (2)

Combining statements (1) and (2):

$\sf{\dfrac{1}{2}\times\:base\times\:height=35000\:m^2}$

We know that the length of the base is 350 m.

$\sf{=\dfrac[1}{2}\times350\times\:height=35000\:m^2}$

$\sf{=175\times\:height=35000\:m^2}$

$\sf{height=\dfrac{35000}{175}}$

$\sf{height=200\:m}$

Hence the altitude of the triangular field is 200 m.