Question

Help me quick!! A rancher has a field in the shape of the polygon shown.

Answer 1

The area of the field is 36,000m², and in that area he can have 18 sheeps.

How many sheeps can he have in that field?

To find the area of the field, we can find the area of a square of 200m by 200m, and then subtract the area of a triangle of base of 100m and height of 80m.

The area of the square is:

S = 200m*200m = 40,000m²

The area of the triangle is:

T = 100m*80m/2 = 4,000m²

Then the area of the field is:

Area = 40,000m² - 4,000m² = 36,000m²

and each sheep needs 2,000m², then the number of sheeps that she can has is:

N = 36,000m²/2,000m² = 18

Answer 2

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Answer:

18 sheep

Explanation:

The triangle cut from the upper right corner has a height of 200-100=100 m and a width of 200-120=80 m. Its area is given by the triangle area formula ...

A = 1/2bh

A = 1/2(80 m)(100 m) = 4000 m²

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The area of the square that includes that triangle is ...

A = LW

A = (200 m)(200 m) = 40000 m²

So, the area of the field where the farmer can keep sheep is ...

field area = 40000 m² -4000 m² = 36000 m²

At 2000 m² per sheep, the field will support ...

(36000 m²)/(2000 m²/sheep) = 18 sheep