Question

HERON'S FORMULA
5. 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
207
cow be getting?
6. An umbrella is made by stitching 10 trinoul​

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=

s(s−a)(s−b)(s−c)

=

54(54−48)(54−30)(54−30)

=

54×6×24×24

=

72×6

=432m

2

⇒Area of field

=2× Area of ΔBCD

=2×432 m

2

=864 m

2

⇒Area of grass field each cow be getting

=

18

864

=48 m

2

Answer 2

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Here, AB = BC = CD = DA = 30 m and Diagonal AC = 48 m which divides the rhombus ABCD in two congruent triangle.

Here, AB = BC = CD = DA = 30 m and Diagonal AC = 48 m which divides the rhombus ABCD in two congruent triangle.Area of ABC = Area of ACD

Semi perimeter of ABC. = 30+30+48/2. = 54m

Now Area of rhombus ABCD = Area of ABC + Area of ACD

Now Area of rhombus ABCD = Area of ABC + Area of ACD= 2 Area of ABC [ Area of ABC = Area of ACD]

$\sqrt{54 \times (24) \times (24) \times (6)}$

$2 \times 3 \times 6 \times 24$

$864 {m}^{2}$

Field available for 18 cows to graze the grass =864m2

Field available for 1 cow to graze the grass = 864/18 = 48m²

$\huge\underline\mathbb{\red F\pink {O}\purple {L} \blue {LO} \orange {W}\green {ME}}$