find the area of the following figures
Answers
To find : Area of given figure
Construction :
- Mark p,q,r,s as shown in attachment
Given :
- Ap = 2cm
- Bp = 3cm
- Aq = 5cm
- Cs = 4cm
- sD = 4.5cm
- rD = 6cm
- Fq= 3cm
- Er = 2cm
- qr = 4cm
Formula used :
- area of trapezium = (1/2) (sum of parallel side ) × distance between them
- area of traingle = (1/2)×base × height
Solution :
The given figure is combination of 4 triangle and 2 trapezium
Therefore
area of figure = sum of area of each individual part
AD = Ap + ps + sD = Aq + qr + rd
=> 2 + ps + 4.5 = 5 + 4 + 6
=> ps = 15 - 6.5
=> ps = 8.5cm
(1) Area of triangle ABp = (1/2) × Ap × pB
=> Area of ∆ABp = (1/2)×2×3
=> Area of ∆ABp = 3cm²
(2) Area of trapezium BCsp = (1/2) × (Bp+Cs)×(ps)
=> Area of trapezium BCsp = (1/2) ×(3+4)×(8.5)
=> Area of trapezium BCsp = 29.75cm²
(3) Area of triangle CDs = (1/2) × (Cs)×(sD)
=> Area of ∆CDs = (1/2)×4×4.5
=> Area of ∆CDs = 9cm²
(4) Area of ∆DEr = (1/2) Dr × Er
=> Area of∆DEr = (1/2) × 6×2
=> Area of ∆DEr = 6cm²
(5) Area of trapezium EFqr = (1/2)×(Er + Fq) × (qr)
=> Area of trapezium EFqr = (1/2)×(3+2)×4
=> Area of trapezium EFqr = 10cm²
(6) Area of ∆AFq = (1/2)×(Aq)×(Fq)
=> Area of ∆AFq = (1/2)×(5)×(3)
=> Area of ∆AFq = 7.5cm²
Area of figure = area of ( 1+2+3+4+5+6)
Area of figure = (3+29.75+9+6+10+7.5)cm²
Area of figure = 65.25cm²
ANSWER : Area of figure = 65.25cm²
