Question

Estimate the perimeter and area of the shaded figure to the nearest tenth.

perimeter: about ? units
area: about ? square units

Answer 1

Perimeter = 18.7 units

Area = 13.5 units²

Explanation:

Perimeter of ADEC = AD + DE + EC + AC

Length of AD = 3 units

By applying Pythagoras theorem in ΔDBE,

DE² = DB² + BE²

DE² = 3² + 3²

DE = √18

DE = 4.24 units

Length of EC = 3 units

By applying Pythagoras theorem in ΔABC,

AC² = AB² + BC²

AC² = 6² + 6²

AC = √72

AC = 8.49 units

Perimeter of ADEC = 3 + 4.24 + 3 + 8.49

= 18.73 units

≈ 18.7 units

Area of ADEC = Area of ΔABC - Area of ΔBDE

Area of ΔABC =
`(1)/(2)(AB)(BC)`

=
`(1)/(2)(6)(6)`

= 18 units²

Area of ΔBDE =
`(1)/(2)(BD)(BE)`

=
`(1)/(2)(3)(3)`

= 4.5 units²

Area of ADEC = 18 - 4.5

= 13.5 units²