find the area of a quadrilateral PQRS in which PQis equal to 3cm , QR is equal to 4cm ,RS is equal to 4cm, SP is equal to 5cm and PR is equal to 5cm
Answers
Answered by
1
Answer:
Step-by-step explanation:
you can use the area of a quadrilateral formula that is 1/2*sum of perpendiculars *height
Answered by
0
Answer:
In quadrilateral ABCD,
AB=3 cm,BC=4 cm,CD=2 cm,DA=5 cm and ∠ABC=90
0
Area of ABCD = Area of ΔABC+ Area of ΔACD
In ΔABC,∠B=90
0
∴ Area of ΔABC =
2
1
×AB×BC=
2
1
×3×4 cm
2
=6cm
2
In ΔABC, applying pythagorous theorem we get,
AC
2
=AB
2
+BC
2
⇒AC
2
=3
2
+4
2
⇒AC
2
=9+16
⇒AC
2
=25
⇒AC=5
∴AC=5 cm
In ΔACD, semi-perimeter s=
2
2+5+5
cm=6 cm
Applying Heron's formula,
Area of Δ ACD =
S(S−a)(S−b)(S−c)
=
6(6−5)(6−5)(6−2)
=
6(1)(1)(4)
=
24
Hence, Area of □ABCD=(6+
24
)cm
2
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