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

apid Theory you need to know! eview

Perimeter of a rectangle = 2 (Length + Breadth)

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(4a² − b²)
= 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.

Related Links in Math - Geometry Lesson Plans :

Math - Geometry Lesson Plans : Perimeter & Area of Triangles

Math - Geometry Lesson Plans : Perimeter & Area of Rectangles & Squares