Isosceles Trapezoid

An isosceles trapezoid is a type of quadrilateral with a line of symmetry bisecting one pair of opposite sides, making it automatically a trapezoid. Two opposite sides (bases) are parallel, the two other sides (legs) are of equal length. The diagonals are of equal length. An isosceles trapezoid's base angles are equal in measure. Any quadrilateral with exactly one axis of symmetry must be either an isosceles trapezoid or a kite [Source: wikipedia]

Example 1:

Find the area of an isosceles trapezoid with sides is 6 cm, bases 4 cm and 10 cm, and altitude 8 cm?

Solution:

Area of the trapezoidal = h* (b1+b2)/2

Where h = altitude of the trapezoidal

b1, b2 = base of the trapezoidal

From the problem h=8 cm b1= 4 cm and b2 = 10 cm

Area = 8 * (4+10)/2

Area = 8 * 14 /2

Area = 56 cm2

Example 2:

Find the area of an isosceles trapezoid with bases 6 cm and 8 cm Side AB= 12 cm?

Solution:

Area of the trapezoidal =  `sqrt((s-a)*(s-b)*(s-c))`

Where s = `(a+b+2c)/(2)` (or) s =`(a+b)/(2)` + c

Area of the trapezoidal =   `sqrt(((a+b)^2 (a-b+2c)(b-a+2c))/(16))`

From the problem a= 6 cm b= 8 cm c= 12 cm

S = 6+8+2(12)/2

S= 14+24/2

S=38/2

S= 19 cm

S-a = 19-6 = 13 cm

S-b=19-8=11 cm

S-c=19-12 = 7cm

Area = `sqrt(13*11*7^2)`

=`sqrt(13*11*49)`

=`sqrt(7007)`

=83.70 cm2

Example 3:

Find the area of an isosceles trapezoid with sides is 18 cm, bases 12 cm and 14 cm, and altitude 16cm?

Solution:

Area of the trapezoidal = h* (b1+b2)/2

Where h = altitude of the trapezoidal

B1, b2 = base of the trapezoidal

From the problem h=16 cm b1= 12 cm and b2 = 14 cm

Area = 16 * (12+14)/2

Area = 16 * 26 /2

Area = 208 cm2

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Example 4:

Find the altitude of an isosceles trapezoid with sides is 4 cm, bases 5cm and 8cm, and area = 160cm2?

Solution:

Area of the trapezoidal = h* (b1+b2)/2

Where h = altitude of the trapezoidal

B1, b2 = base of the trapezoidal

From the problem b1= 5 cm and b2 = 8 cm, area = 160cm2

160 = h * (5+8)/2

160= h * 13/2

H=160*2/13

H=24.62 cm