Find the area of the hexagon ABCDEF in which AC=8cm,CD=4cm,BM=3cm,NE=10.2,DO=5cm,AF=8.4cmb,OP=3.2cm.
Answers
Answer:
24√3
Step-by-step explanation:
AC=8
AB=1/2×AC
=1/2×8
AB=4
A(hexagon)=6×√3/4×side×side
= 6×√3/4×4×4
= 24
The area of hexagon ABCDEF is 75.4 cm².
Step-by-step explanation:
Required Formulas:
- Area of triangle = ½ × (base) × (height)
- Area of rectangle = length × breadth
It is given that,
In a hexagon ABCDEF, we have
AC = 8cm, CD = 4cm, BM = 3cm, NE = 10.2, DO = 5cm, AF = 8.4 cm and OP = 3.2cm.
Referring to the figure attached below, we get
FP = AN = AC – CN = AC - OD = 8 - 5 = 3 cm
EP = NE – NP = NE - AF = 10.2 – 8.4 = 1.8 cm
OE = NE – ON = NE – CD = 10.2 - 4 = 6.2 cm
Also we can see that,
Area (Hexagon ABCDEF) is given by,
= area ( ΔABC) + area ( ΔFPE) + area ( ΔDOE) + area (Rect. ANPF) + area (Rect. CDON) …… (i)
Now,
Area (Δ ABC) = ½ × (BM) × (AC) = ½ × (3) × (8) = 12 cm² ….. (ii)
Area (Δ FPE) = ½ × (FP) × (EP) = ½ × (3) × (1.8) = 2.7 cm² …….. (iii)
Area (Δ DOE) = ½ × (OD) × (OE) = ½ × (5) × (6.2) = 15.5 cm² …….. (iv)
Area (Rect. ANPF) = AF × FP = 8.4 × 3 = 25.2 cm² …… (v)
Area (Rect. CDON) = CD × OD = 4 × 5 = 20 cm²…… (vi)
Thus, substituting values from (ii), (iii), (iv), (v), (vi) in (i), we get
The area of hexagon ABCDEF as,
= 12 + 2.7 + 15.5 + 25.2 + 20
= 75.4 cm²
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Also View:
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