Question

what is the area of trapezium whose parallel side are 15 cm and 23cm non parallel side are 8 and 10 cm. explain step by step. ​

Answer 1

Given : trapezium whose parallel side are 15 cm and 23cm non parallel side are 8 and 10 cm

To Find :  area of trapezium

Solution:

Let say ABCD is trapezium

with AB || CD

AB = 23 cm  & CD = 15 cm

AD =  10 cm   & BC = 8 cm

Draw DM & CN ⊥ AB  => DM = CN

MN = 15 cm

Let say AM = x  cm  then  BN 23-15 - x  = 8 - x cm

DM² = AD² - AM² = 10² - x²

CN² = BC² - BN² = 8² - (8-x)²

DM² = CN²

=> 10² - x²  =  8² - (8-x)²

=> 100 - x² = 64 - (64 + x²  - 16x)

=> x = 100/16

=> x= 6.25

DM² =  10² - x²  = 10² - 6.25² = 60.9375

=> DM = 7.806

Area of trapezium = (1/2) (15 + 23) * 7.806

= 148.31 cm²

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Answer 2

Question:

what is the area of trapezium whose parallel side are 15 cm and 23cm non parallel side are 8 and 10 cm. explain step by step.

Given:

Trapezium whose || side are 15cm and 23cm

non-|| side are 8cm and 10cm

To Find:

Area of Trapezium

Solution:

Let the ABCD is trapezium with AB||CD

AB= 24cm & CD= 15cm

AD=10cm & BC= 8cm

Draw DM & CN perpendicular to Ab => DM = CN

MN = 15cm

Let say AM= x cm then BN=> 23-15-x = 8-x cm

DM² = AD²-AM² => 10²-x²

CN² = BC²-BN² => 8²-(8-x)²

DM² = CN²

=> 10² - x² = 8²-(8-x)²

=> 100-x² = 64-(64+x²-16x)

=> x = 100/16

=> x = 6.25

DM² = 10²-x²

=> 10²-6.25²= 60.9375

DM = √60.9375

DM = 7.806

Area of Trapezium= (1/2)(15+23)*7.806

= 148.31cm²