Understand the area of of trapezium with the help of a Numerical problem. click on the link to Watch the VIDEO explanation: Watch Video
Numerical
The two parallel sides of a trapezium are 56 cm and 40 cm respectively
The other non - parallel sides are 17 cm each. Find the area of trapezium.
Let us represent this by a diagram
To proceed with this problem, we need to make two constructions in the diagram. Can you pick the correct answer from the given choices
Draw a line BD parallel to AD to meet Dc at E and draw a perpendicular from B to meet DC at F. Now ABED is a parallelogram.
Therefore, AD is equal to BE which is equal to 17 cm
DE is equal to AB which is equal to 40 cm
Therefore, EC is equal to DC minus DE which is equal to 56 minus 40 which is equal to 16 cm.
Consider triangle BEC
s is equal to Perimeter of triangle BEC by 2 which is equal 17 plus 17 plus 16 by 2 which is equal50 by 2 which is equal 25.
Area of triangle BEC is equal to root of s into s minus a into s minus b into s minus c
Calculate and key in your answer in the text box. Click on check to verify your answer.
Therefore, Area of triangle BEC is equal to 120 cm square.
Now, we need to find the value of BF.
Area of triangle BEC is equal to half into base into height this is equal to half into EC into BF which is equal to 120 cm square as we have already calculated.
Therefore, half into EC into BF is equal to 120. Calculate the value of BF and enter in the text box. Cleck check to verify.
Therefore, BF is equal to 15 cm.
Now, let us calculated the area of trapezium ABCD
Can you pick the formula for area of the trapezium from the choices below
Area of trapezium is equal to half into AB plus DC into BF.
Calculate the Area of trapezium ABCD and enter the value in the text box. . Click check to verify your answer.
Therefore area of trapezium ABCD is equal to 720 square cm.
Numerical
The two parallel sides of a trapezium are 56 cm and 40 cm respectively
The other non - parallel sides are 17 cm each. Find the area of trapezium.
Let us represent this by a diagram
To proceed with this problem, we need to make two constructions in the diagram. Can you pick the correct answer from the given choices
Draw a line BD parallel to AD to meet Dc at E and draw a perpendicular from B to meet DC at F. Now ABED is a parallelogram.
Therefore, AD is equal to BE which is equal to 17 cm
DE is equal to AB which is equal to 40 cm
Therefore, EC is equal to DC minus DE which is equal to 56 minus 40 which is equal to 16 cm.
Consider triangle BEC
s is equal to Perimeter of triangle BEC by 2 which is equal 17 plus 17 plus 16 by 2 which is equal50 by 2 which is equal 25.
Area of triangle BEC is equal to root of s into s minus a into s minus b into s minus c
Calculate and key in your answer in the text box. Click on check to verify your answer.
Therefore, Area of triangle BEC is equal to 120 cm square.
Now, we need to find the value of BF.
Area of triangle BEC is equal to half into base into height this is equal to half into EC into BF which is equal to 120 cm square as we have already calculated.
Therefore, half into EC into BF is equal to 120. Calculate the value of BF and enter in the text box. Cleck check to verify.
Therefore, BF is equal to 15 cm.
Now, let us calculated the area of trapezium ABCD
Can you pick the formula for area of the trapezium from the choices below
Area of trapezium is equal to half into AB plus DC into BF.
Calculate the Area of trapezium ABCD and enter the value in the text box. . Click check to verify your answer.
Therefore area of trapezium ABCD is equal to 720 square cm.
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