Question

field is in the form of a right triangle with hypotenuse of 10 and one side is 8 metre find the area of field​

Answer 1

Answer:

HII FRIEND!!!

THE ANSWER IS 24m²

Answer 2

Given:-

hypothenuse (h) = 10m

first side (a) = 8m

second side (b) = ?

Finding the second side:-

By Pythagoras theorem-

=> (hypothenuse)² = (first side)² + (second side)²

=> (h)² = (a)² + (b)²

=> (10m)² = (8m)² + (b)²

=> 100m² = 64m² + b²

=> b² = 100m² - 64m²

=> b² = 36m²

=> b = √(36m²)

=> b = 6m

To find:-

The area of the field.

Formula:-

$area = \sqrt{s(s - a)(s - b)(s - c)}$

Solution:-

So, to find the area with the above formula we have to find the semi - perimeter first.

$Semi - perimeter = \frac{sum \: of \: all \: sides}{2} \\ \\ = \frac{h + a + b}{2} \\ \\ = \frac{10m + 8m+ 6m}{2} \\ \\ = \frac{24m}{2} \\ \\ = 12m$

Now, finding the area.

$area = \sqrt{s(s - a)(s - b)(s - h)} \\ \\ = \sqrt{12m(12m - 8m)(12m - 6m)(12m - 10m)} \\ \\ = \sqrt{12m \times 4m \times 6m \times 2m} \\ \\ = \sqrt{576 {m}^{4} } \\ \\ = 24 {m}^{2}$

Answer:-

The area of the field is 24m².