Given PR = 24 cm, PN = 18 cm, PO = 10 cm, QM = 5 cm, SN = 9 cm, TO = 7 cm. Find
the area of the polygon PQRST.
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Answers
The area of the polygon PQRST is 186 cm²
Given:
PR = 24 cm, PN = 18 cm, PO = 10 cm,
QM = 5 cm, SN = 9 cm, TO = 7 cm.
To find:
Find the area of the polygon PQRST
Solution:
To find the area of the Polygon PQRST
we will divide the polygon into 4 parts as given below
1. ΔPQR, 2. Δ RSN, 3. ΔOPT and 4. trapeziam NOST
Now find the area of each part
1. Area of ΔPQR
=> (1/2) (PR)(MQ)
=> (1/2) (24)(5)
=> 12(5) = 60 cm²
Area of ΔPQR = 60 cm²
2. Area of Δ RSN
=> (1/2)(RN)(SN)
Given PR = 24 cm and PN = 18 cm
=> RN = PR - PN = 24 - 18 = 6 cm
Area of Δ RSN = (1/2)(6)(9)
=> 27 cm²
Area of Δ RSN = 27 cm²
3. Area of ΔOPT
=> (1/2)(PO)(TO)
=> (1/2)(10)(7)
=> 35 cm²
Area of ΔOPT = 35 cm²
4. Trapezium NOST
=> (½) × (TO+ NS) × ON
=> (½) × (7 + 9) × 8
=> (½) × (16) × 8
=> 64 cm²
Area of Trapezium NOST = 64 cm²
From the above calculations,
Area of PQRST = ΔPQR + Δ RSN + ΔOPT + trapeziam NOST
= 60 cm² + 27 cm² + 35 cm² + 64 cm²
= 186 cm²
Therefore,
The area of the polygon PQRST is 186 cm²
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