Question

In quadrilateral ABCD side AB is parallel to side DC, seg AE is perpendicular to seg DC. If line AB is 9 cm , line AE is 10 cm , area of quadrilateral ABCD is 115 cm square. Find line DC.

Answer 1

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As per the question

• AB = 9 cm

• AE = 10 cm

• Area = 115 cm²

• AB || CD

• AE Perpendicular to DC

♦ Now from the given information we can say that ABCD is a Trapezium .

>> Trapezium is a quadrilateral which have One Pair of Parallel Side .

♦ Now we have the area , one of the parallel side's length and length of the perpendicular between two parallels , So as we know that the are of Trapezium is Sum of Parallel sides multiplied by the height .

♦ So , by using the formula

$\implies (AB + CD ) \times (AE) = 115$

$\implies (9 + CD ) \times (10) = 115$

$\implies 90 + 10(CD) = 115$

$\implies 10(CD) = 115 - 90$

$\implies 10(CD) = 25$

$\implies CD = \dfrac{25}{10}$

$\implies CD = 2.5 \: cm$

♦ So the length of DC ( or CD ) = 2.5 cm

Answer 2

Answer:

According to given information ABCD  is Trapezium So  to find l(DC)

Area of Trapezium =1/2 multiply (sum of  lenghts Parallel sides)  multiply Height

Area of TrapeziumABCD= 1/2 multiply (AB +DC) multiply AE (height)

115=1/2 multiply (9+x(DC) multiply 10

115=  9+x multiply 5 (1/2 x10=5)

115=45 +5x

115-45=5x

70=5x

x=14      length DC =14

Step-by-step explanation: