Question

calculate the area of shaded region

Answer 1

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Answer 2

Answer:

The area of shaded region is 54 cm².

Step-by-step explanation:

First we will calculate the side AB by using the Pythagoras theorem:

AB² = BD² + AD²

AB² = 5² + 12²

AB² = 25 + 144

AB² = 169

AB = 13 cm.

Now, we will calculate the Area of triangle ABC:

ΔABC = √s(s-a)(s-b)(s-c)

s = a + b + c / 2

s = 15 + 14 + 13 / 2

s = 42 / 2

s = 21

ΔABC = √21(21-13)(21-14)(21-15)

ΔABC = √21(8)(7)(6)

ΔABC = √7056

ΔABC = 84 cm²

Now, we will calculate the Area of triangle ABD:

s = 12 + 5 + 13 / 2

s = 15

ΔABD = √15(15-13)(15-12)(15-5)

ΔABD = √15(2)(3)(10)

ΔABD = √900

ΔABD = 30 cm²

Area of shaded region = ΔABC  - ΔABD

Area of shaded region =84 cm² - 30 cm²

Area of shaded region = 54 cm²

Therefore, the area of shaded region is 54 cm².

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