Question

FORMULA
207
A rhombus shaped field has green grass for 18 cows to graze. If each side of the
rhombus is 30 m and its longer diagonal is 48 m, how much area of grass field will each
cow be getting?
An umbrella is made by stitching 10 triangular pieces of cloth of two different colours​

Answer 1

Given:

⇒ ABCD is a Rhombus

⇒For ΔBCD

Perimeter

=8+30+30

=108  cm

⇒2S=108  cm, S=54  cm

⇒Area of ΔBCD

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

$= \sqrt{54(54-48)(54-30)(54-30)\\} \\\\\\=\sqrt{54*6*24*24}=\sqrt{72*6}\\ \\= 432m^2$

⇒ Area of field

= 2 × Area of ΔBCD

= 2 × $432m^2$ =  $864m^2$

⇒Area of grass field each cow be getting

$= \frac{864}{18} = 48m^2$

→ $48m^2$

Answer 2

Answer:

48m2

Step-by-step explanation:

Draw a rhombus-shaped field first with the vertices as ABCD. The diagonal AC divides the rhombus into two congruent triangles which are having equal areas.

Consider the triangle BCD,

Its semi-perimeter = (48 + 30 + 30)/2 m = 54 m

Using Heron’s formula,

Area of the ΔBCD = √54 (54 - 48)( 54-30) (54-30)

= 432 m2

∴ Area of field = 2 × area of the ΔBCD = (2 × 432) m2 = 864 m2

Thus, the area of the grass field that each cow will be getting = (864/18) m2 = 48 m2

Hope it helps