Question

Find the area of trapezoid ABCD by decomposing it into a rectangle and triangle.

A)80 cm2
B)96 cm2
C)104 cm2
D)112 cm2

Answer 1

To find the area of trapezoid ABCD, we first need to decompose it into a rectangle and a triangle.

First, let's draw a perpendicular line from point A to line CD. Let's call the point where the perpendicular line intersects CD point E.

This perpendicular line divides the trapezoid into a rectangle (AEDC) and a right triangle (ABE).

The area of the rectangle AEDC is length x width = 8 cm x 10 cm = 80 cm^2.

To find the area of the triangle ABE, we need to find the height (BE) and the base (AB). Using Pythagorean theorem, we find that BE = √(10^2 - 6^2) = 8 cm.

Therefore, the area of triangle ABE is (1/2) x base x height = (1/2) x 6 cm x 8 cm = 24 cm^2.

Finally, the total area of trapezoid ABCD is the sum of the areas of the rectangle and the triangle: 80 cm^2 + 24 cm^2 = 104 cm^2.

So, the correct answer is:

C) 104 cm2