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

Video Transcript

Given that 𝐴𝐵𝐶𝐷 is a parallelogram, find the area of triangle 𝐴𝐵𝑀.

So, here, we’re given this parallelogram 𝐴𝐵𝐶𝐷. And we need to find the area of this triangle 𝐴𝐵𝑀. In order to do this, we’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 𝐶𝐷 is parallel and equal in length to the line 𝐴𝐵. In the same way, the other two sides — that is, 𝐴𝐷 and 𝐶𝐵 — are equal and parallel. We could then write that the length 𝐴𝐷 must also be 20 centimeters.

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

To find the area of 𝐴𝐵𝑀, we’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 𝐴𝐵𝑀 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 we’re dealing with an area. And so, our answer is that the area of triangle 𝐴𝐵𝑀 is 55 square centimeters.