Question

A farmer has a triangular field with sides 240 m, 200 m and 360 m, where he grew wheat. In another triangular field with sides 240 m, 320 m and 400 m adjacent to the previous field, he wanted to grow potatoes and onions (see figure). He divided the field into two parts by joining the mid point of the longest side to the opposite vertex and grew potatoes in one part and onions in the other part. How much area (in hectares) has been used for wheat, potatoes and onions? Now 10,000 m2 = 1 hectare

Answer 1

Answer:

Potatoes = 1.92 Hectare

Onion = 1.92 hectare

Wheat = 2.26 Hectare

Step-by-step explanation:

Area of Triangle with sides

240 m, 200 m and 360 m   for Wheat

s = (240 + 200 + 360)/2 = 400

Area using hero Formula

= √400 (400-240)(400-200)(400-360)

= √400 * 160 * 200 * 40

= 16000√2 m²

=1.6√2 hectare

= 2.26 Hectare

Area of Triangle with sides

240 m, 320 m and 400 m   for onion & Potato

s = (240 + 320 + 400)/2 = 480

Area = √480 * 240 * 160 * 80

= 38400 m²

= 3.84 Hectare

divided the field into two parts by joining the mid point of the longest side to the opposite vertex i.e Median

Median Divides the triangle into two equal area

= 3.84/2

= 1.92 Hectare

Potatoes = 1.92 Hectare

Onion = 1.92 hectare

Wheat = 2.26 Hectare

Answer 2

Answer:

Area for Potatoes Cultivation = 1.92 Hectare

Area for Onion Cultivation = 1.92 hectare

Area for Wheat Cultivation = 2.26 Hectare

Step-by-step explanation:

The sides of the given triangles are:

Wheat cultivation - 240 m, 200 m and 360 m  

We use Herons Formula to solve this problem:

Semi - Perimeter = (240 + 200 + 360) / 2

=> 400

Now,

Finding Area by using Herons Formula:

$=>\sqrt{400(400-240)(400-200)(400-360)}$

$=>\sqrt{(400)(160)(200)(40)}$

$=>16000\sqrt{2}m^{2}$

Converting Meter to Hectare:

1 Meter = 1 / 10,000 Hectare

$=>16000\sqrt{2}m^{2}$ / 10,000

$=>1.6\sqrt{2} hectare$

=> 1.6 * 1.414                  (Substituting the value of $\sqrt{2}$ as 1.414)

=> 2.26 Hectare (approx.)

Area of the other Triangle which has the side measures as:

=> 240 m, 320 m and 400 m  

These measures are for calculating area required for Onions and Potatoes cultivation.

Again we use Herons Formula here:

Semi - Perimeter = (240 + 320 + 400) / 2 = 480

Area required for Onions and Potatoes$\sqrt{(480)(240)(160)(80)}$

$=>\sqrt{(480)(240)(160)}$

= 38,400 m²

Again Converting Meters to Hectares:

=> 38,400 / 10,000

=> 3.84 Hectares

Now, we divide the field into two parts by joining the mid - point of the longest side to the opposite vertex the Median as per the question. Median  of a triangle divides the triangle into two equal parts and therefore the area of these equal parts will also be equal.

=> 3.84/2

=> 1.92 Hectare

Therefore, the final answer is as follows:

Area required for Potatoes Cultivation = 1.92 Hectares.

Area required for Onions Cultivation = 1.92 Hectares.

Area required for Wheat Cultivation = 2.26 Hectares.