Question Video: Finding the Area of a Triangle Drawn on Half the Base of a Given Parallelogram | Nagwa Question Video: Finding the Area of a Triangle Drawn on Half the Base of a Given Parallelogram | Nagwa

# Question Video: Finding the Area of a Triangle Drawn on Half the Base of a Given Parallelogram Mathematics

Given that π΄π΅πΆπ· is a parallelogram, find the area of triangle π΄π΅π.

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### Video Transcript

Given that π΄π΅πΆπ· is a parallelogram, find the area of triangle π΄π΅π.

So, here, weβre given this parallelogram π΄π΅πΆπ·. And we need to find the area of this triangle π΄π΅π. In order to do this, weβll need to recall a fact about parallelograms. And that is that a parallelogram has two pairs of parallel and congruent sides. So therefore, the line πΆπ· is parallel and equal in length to the line π΄π΅. In the same way, the other two sides β that is, π΄π· and πΆπ΅ β are equal and parallel. We could then write that the length π΄π· must also be 20 centimeters.

In order to find this length of π΄π, we observe the demarcations on the lines here at ππ· and π΄π, which means that these lengths are the same size. This means that our 20-centimeter length of π΄π· must be split into two equal sections of 10 centimeters each.

To find the area of π΄π΅π, weβll need to recall the formula for the area of a triangle. The area of a triangle is equal to half times the base times the perpendicular height. Looking at triangle π΄π΅π in the diagram, we can take the base as 10 centimeters. And the perpendicular height here would be 11 centimeters. Looking at the calculation a half times 10 times 11, we can take a half of 10 as five. And then, five times 11 gives us 55. And the units here would be in squared centimeters since weβre dealing with an area. And so, our answer is that the area of triangle π΄π΅π is 55 square centimeters.

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