Question

3. The trapezoid below contains a square and two right triangles. Find the perimeter of the trapezoid.

Answer 1

Perimeter of trapezoid = 25.66 cm

Explanation:

Trapezoid ABCD contains two triangles ΔABF, ΔCDE and a square with side length 4 cm.

By applying Pythagoras theorem in ΔABF,

AB² = BF² + AF²

AB² = 4² + 3²

AB =
`√(16+9)`

AB = 5 cm

Similarly, By applying Pythagoras theorem in ΔCDE,

CD² = DE² + CE²

CD² = 4² + 4²

CD =
`√(32)`

CD =5.66 cm

Perimeter of the given trapezoid = AB + BC + CD + AD

= 5 + 4 + 5.66 + (3 + 4 + 4)

= 25.66 cm