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mihalych1998 [28]
3 years ago
15

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

Mathematics
1 answer:
Maru [420]3 years ago
6 0

Answer:

Perimeter = 18.7 units

Area = 13.5 units²

Step-by-step 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 = \frac{1}{2}(AB)(BC)

                       = \frac{1}{2}(6)(6)

                       = 18 units²

Area of ΔBDE = \frac{1}{2}(BD)(BE)

                       = \frac{1}{2}(3)(3)

                       = 4.5 units²

Area of ADEC = 18 - 4.5

                        = 13.5 units²

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