### Video Transcript

π΄π΅πΆπ· is a trapezoid where the
lengths of its parallel bases π΄π· and π΅πΆ are 36 centimeters and 48 centimeters,
respectively. The length of the perpendicular
drawn from π· to π΅πΆ is 35 centimeters. Find the area of π΄π΅πΆπ·, giving
your answer to the nearest square centimeter.

In this question, weβre told that
π΄π΅πΆπ· is a trapezoid. We can see this from the diagram as
we have a pair of parallel sides. So, we know it is a trapezoid. Weβre told that the bases π΄π· and
π΅πΆ are 36 and 48 centimeters, and thatβs on the diagram. Weβre also told that the
perpendicular drawn from π· to π΅πΆ is 35 centimeters, and thatβs also on the
diagram. Importantly, it also tells us that
the height of this trapezoid is 35 centimeters.

To find the area of π΄π΅πΆπ·, weβre
going to use the formula to find the area of a trapezoid. This formula tells us that the area
of a trapezoid is equal to a half β times π sub one plus π sub two, where β is the
height of the trapezoid and π sub one and π sub two are the bases or parallel
sides of the trapezoid. So to find the area of π΄π΅πΆπ·, we
plug in the values that we have. The height is 35 centimeters. π sub one and be π sub two are 36
and 48, and it doesnβt matter which way around these are. So, for the area, weβre calculating
a half times 35 times the sum of 36 and 48. We can simplify 36 plus 48 to give
us 84.

As it doesnβt matter which way we
multiply, it might seem sensible to find half of 84 rather than half of 35. This means weβre working out 35
times 42. Without a calculator, we could work
this out as 1,470. And the units here will be square
units of square centimeters. We were asked for an answer to the
nearest square centimeter, but we have an integer value here, so we donβt need to
round. Therefore, π΄π΅πΆπ· has an area of
1,470 square centimeters.