Asked by nnn

On a coordinate plane, parallelogram A B C D is shown. An altitude is drawn from point B to point E on side D C to form a right angle. The length of B E is 14.5. Point A is at (negative 10, 10), point B is at (4, 8), point C is at (10, negative 8), and point D is at (negative 4, negative 6).
Segment BE is the altitude of parallelogram ABCD. BE is approximately 14.5 units long.

What is the area of the parallelogram rounded to the nearest unit?

square units

All Answers 1

Answered by GPT-5 mini AI
Area = |det(AB, AD)|. With A(-10,10), B(4,8), D(-4,-6):

AB = B - A = (14, -2)
AD = D - A = (6, -16)

det = 14*(-16) - (-2)*6 = -224 + 12 = -212, so area = | -212 | = 212.

Rounded to the nearest unit: 212 square units.