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# Math - Geometry Lesson Plans : Perimeter & Area of Quadrilaterals II apid Theory you need to know! eview

Mensuration - Formulae for Perimeter and Area of Quadrilaterals II

Perimeter of a rectangle = 2 (Length + Breadth)

 Diagonal of a rectangle = Ö Length2 + Breadth2

Area of a rectangle = Length × Breadth

Perimeter of a square = 4 × Side

Diagonal of a square = Ö2 Side

Area of a square = Side2

Area of a square = ½ × Diagonal2

Area of a quadrilateral when diagonals intersect at right angles = ½ × Product of diagonals

Area of a quadrilateral when one diagonal and the lengths of the perpendiculars from its opposite vertices to this diagonal are given = ½ × Diagonal × Sum of the lengths of the perpendiculars

Area of a parallelogram = Base × Height

Area of a rhombus = ½ × Product of diagonals

Area of a trapezoid = ½ × Sum of parallel sides × Distance between parallel sides Example
Calculate the perimeter (in cm) of the quadrilateral EFGH in which EF = 42 cm, GH = 74 cm, EH = 56 cm, FH = 70 cm and ∠GFH = 90°.
Solution. In ΔFGH, by Pythagorean Theorem, GH2 = FG2 + FH2
∴ FG2 = GH2 − FH2 = 742 − 702 = 576 or FG = 24 cm.
Perimeter of the quadrilateral = EF + FG + EH + GH = 42 + 24 + 56 + 74 = 196 cm. Example
Find the area (in cm2) of the quadrilateral PQRS in which PQ = 36 cm, QR = RS = 50 cm, PS = 48 cm and ∠QPS = 90°.
Solution. By Pythagorean Theorem, QS2 = PQ2 + PS2
= 362 + 482 = 3600 or QS = 60 cm.
Area of ΔPQS = ½ × Base × Height
= ½ (36) (48) = 864 cm2.
Area of isosceles ΔQRS = ¼ b Ö(4a2b2)
= ¼ (60) Ö(4 × 502 − 602) = 1200 cm2.
Area of the quadrilateral = Area of ΔPQS + Area of ΔQRS
= 864 + 1200 = 2064 cm2. Example
Find the area (in cm2) of the trapezoid ABCD in which AB = 22 cm, BC = 50 cm, CD = 8 cm and ∠BAD = ∠ADC = 90°.
Solution. Construction: Draw CE ⊥ AB. Then, AE = 8 cm.
∴ BE = 22 − 8 = 14 cm.
By Pythagorean Theorem, BC2 = BE2 + CE2
∴ CE2 = BC2 − BE2 = 502 − 142 = 2304 or CE = 48 cm.
Area of ΔBCE = ½ × Base × Height
= ½ × 48 × 14 = 336 cm2.
Area of rectangle ADCE = Length × Breadth
= 48 × 8 = 384 cm2.
Area of the trapezoid = Area of ΔBCE + Area of rectangle ADCE
= 336 + 384 = 720 cm2. Example
The shaded region of the given figure is a villa 68 m long and 24 m broad. It is bordered by a lawn of uniform breadth 6 m on three sides. Find the total area (in m2) occupied by the villa and the lawn.
Solution. Total area occupied by the villa and the lawn = Length × Breadth
= 80 × 30 = 2400 m2.

Math - Geometry Lesson Plans : Practice Exercise for Perimeter & Area of Quadrilaterals II

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