Suman had a triangular field of sides 220m, 180m, and 300m. She purchased adjacent triangular field with sides 300m, 350m and 400m. Find the total area of the two fields.
Answers
Answer:
Semiperimeter of 1st triangle = (220+180+300)/2 = 350
Area of 1st triangle = 350(350-220)
(350-180) (350-300) = √350 130 170"50 = ✓386750000 =19665.96
Semiperimeter of 2nd triangle = (1050)/2
= 525
Area of 2nd triangle = /525(525-300)
(525-350)(525-400) = 525 225 175 125 = √2583984375 = 50832.91
Total area = 19665.96+50832.91 = 70498.87sq.m
Given :
- Sides of the first field = 220m, 180m, and 300m.
- Sides of the second field = 300m, 350m, and 400m.
To find :
- the total area of the two fields.
Solution :
⇒ Let's find the Area of the first field.
Semi-Perimeter = a + b + c/2
= 220 + 180 + 300/2
= 700/2
= 350 m
Area of field = √s(s - a) (s - b) (s - c)
= √350 (350 - 220) (350 - 180) (350 - 300)
= √350 (130) (170) (50)
= √350 × (130) × (170) × (50)
= √386750000
= 19665.96 m²
⇒ Let's find the Area of the second field.
Semi-Perimeter = a + b + c/2
= 300 + 350 + 400/2
= 1050/2
= 525 m
Area of field = √s(s - a) (s - b) (s - c)
= √525 (525 - 300) (525 - 350) (525 - 400)
= √525 (225) (175) (125)
= √525 × (225) × (175) × (125)
= √2583984375
= 50832.90 m²
⇒ Now, let's add the area of the two fields.
Total Area = Area of first field + Area of second field
= 19665.96 + 50832.90
= 70498.86 m²
Therefore, the total area of the two fields is 70498.86 m².