What is the area of quadrilateral ABCD?

The length of AB is 9, BC is 5, CD is 12, and AD is 10. When angle BCD is 90 degrees, what is the area of quadrilateral ABCD? #sat #act #trigonometric #math #sine #cosine #digitalsat

[@LuisdeBritoCamacho]

BD^2 = 25 + 144 = 169 ; BD = 13
Triangle [BCD] Area = (5 * 12) / 2 = 30
Triangle [ABD] Area (using Heron's Formula for : 9 / 10 / 13) = 44,9 ~ 45
Quadrilateral Area = 30 + 45 = 75 Square Units (approx.)

[@JacekiElzbietaWojutynscy]

Error: triangle ABD (9,10,13) is not a right triangle.
It should be rectangular.

[@SATMathPrepLTP]

Hello, the video does not specify that triangle ABD is a right triangle. Instead, the area of triangle ABD is determined using Heron’s formula. Thank you.

[@JacekiElzbietaWojutynscy]

Error: triangle ABD (9,10,13) is not a right triangle.
It should be rectangular.

[@murtadah6327]

But triangle bcd is a right angle triangle. From this, bd and the area of bcd can be had. Once bd is known, area of triangle abd is calculated by Heron’s formula. Adding the two areas will yield the final result.