Question

Find the area of the parallelogram, trapezoid, rhombus, or kite. Round to the nearest tenth, if necessary.

14 yd
7 yd
45°

Answer 1

• sin45=H/7
• H=7/√2
• H=4.95yd

Area =

• Base×Height
• 4.95(14)
• 69.3yd²

Answer 2

• 69.3 yd²

Explanation:

Area equation of the parallelogram

• A = bh, where b- base, h - height

Looking at the picture, we can see the right triangle is isosceles as one of interior angles is 45°. It has hypotenuse of 7 and legs of h.

As per property of 45° right triangle the hypotenuse is √2 times the leg.

It gives us

• h√2 = 7 ⇒ h = 7/√2 = 4.95 (rounded)

Now find the area

• A = 14*4.95 = 69.3 yd²