Question

In the following figure calculate the area of the shaded portion where angle D is right angle


A. 6 sq cm
B. 12 sq cm
C. 6 cm
D. 12 cm

Answer 1

Answer:

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B. 12 sq cm

Answer 2

Alright, to solve this we will use heron's formula, but for that we need the 3rd side AB

We can obtain its value by applying Pythagoras' Theorom in the Triangle ADB

Given:

AD = 3cm

BD = 4cm

We know Hypotenuse^2 = Base^2 + Arm^2

AB^2 = BD^2 + AD^2

AB^2 = 3^2 + 4^2

AB^2 = 9 + 16

AB^2 = 25

AB = 5

Now, we know the values of all 3 sides of triangle ABC, so we can use heron's formula

semiperimeter = (A+B+C)/2 = (5+5+6)/2 = 8

Now, applying heron's formula

Area = √s(s-A)(s-B)(s-C)

= √8(8-5)(8-5)(8-4)

= √288

= 17cm^2

Now, we calculate the area of ADB = 1/2 * b * h

= 1/2 * 4 * 3

= 6 cm^2

So, we get the area of shaded region as 17cm^2 - 6cm^2 = 11cm^2

Our answer will be 11cm^2, and the closest to that from the given options is option B(12 cm^2).

Thus Option B is correct