find the area of pentagon abcde as shown In the given picture. It is given that ap=25cm,pq=15cm,qr=40cm,rd=56cm,bp=20cm,eq=60cm and rc=52cm where bp,eq and cr are perpendicular on ad from b,e and c respectively
Answers
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The area of pentagon ABCDE is 8646 cm².
Step-by-step explanation:
Required Formulas:
- Area of triangle = ½ × (base) × (height)
- Area of rectangle = length * breadth
It is given that,
In a pentagon ABCDE, we have
AP = 25 cm, PQ = 15 cm, QR = 40 cm, RD = 56 cm, BP = 20 cm, EQ = 60 cm and RC = 52 cm.
Referring to the given figure, we can calculate
AD = AP + PQ + QR + RD = 25 + 15 + 40 + 56 = 136 cm
PR = PQ + QR = 15 + 40 = 55 cm
Also we can see that,
Area (Pentagon ABCDE) is given by,
= area ( AED) + area (ABP) + + area ( DRC) + area (rectangle PRCB) …… (i)
Now,
Area (Δ AED) = ½ × (EQ) × (AD) = ½ × (60) × (136) = 4080 cm² ….. (ii)
Area (Δ ABP) = ½ × (BP) × (AP) = ½ × (20) × (25) = 250 cm² …….. (iii)
Area (Δ DRC) = ½ × (RC) × (RD) = ½ × (52) × (56) = 1456 cm² …….. (iv)
Area (rect. PRCB) = RC × PR = 52 × 55 = 2860 cm² …… (v)
Thus, substituting values from (ii), (iii), (iv) & (v) in (i), we get
The area of pentagon ABCDE as
= 4080 + 250 + 1456 + 2860
= 8646 cm².
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