The length of one of the diagonals of a field in the form of a quadrilateral is 42 m. The perpendicular distance of the other two vertices from this diagonal are 12m and 9 m (as shown in figure 1). Find the area of the field.
Answers
✬ Area = 441 m² ✬
Step-by-step explanation:
Given:
- Diagonal of quadrilateral is of 42 m.
- Perpendicular distance from other two vertices on this diagonal are 12 and 9 m.
To Find:
- What is the area of field ?
Solution: Let ABCD be a field in form of quadrilateral in which
- AC = Diagonal (42 m)
- DE = Perpendicular (12 m)
- BF = Perpendicular (9 m)
As we know that
★ Area of ∆ = 1/2(Base)(Height) ★
In ∆ADC
➟ Area of ∆ADC = 1/2(AC)(DE)
➟ 1/2(42)(12) m²
➟ 21(12) m²
➟ 252 m²
Similarly , In ∆ABC
➟ Area of ∆ABC = 1/2(AC)(BF)
➟ 1/2(42)(9) m²
➟ 21(9) m²
➟ 189 m²
So, total area of ABCD = ar(ADC + ABC)
➮ Area of ABCD = (252 + 189) m²
➮ 441 m²
Hence, the area of field is 441 m².
Answer:
Area of the field is 441 m²
Step-by-step explanation:
Area of triangle = 1/2 × base × height
Given that the length of one of the diagonals of a field in the form of a quadrilateral is 42 m. The perpendicular distance of the other two vertices from this diagonal are 12m and 9 m.
Taking 12 m as perendicular and 42 m as height.
Area of triangle = 1/2 × 42 × 12
= 42(6)
= 252 m² ..............(1)
Taking 9 m as perpendicular and 42 m as height.
Area of triangle = 1/2 × 42 × 9
= 21(9)
= 189 m² ...............(2)
Area of the field = (1) + (2)
= (252 + 189) m²
= 441 m²
Hence, the area of the field is 441 m².