What is the total area of the two shapes?

2 nd Option

the total area of the two shapes = 21 square units

Step-by-step explanation:

To find the area of square

From the figure we get one side of square equal to 3√2.

Consider the triangle with hypotenuse as side of square.

Angles are 45°, 45° and 90°, then sides 3 , 3 and 3√2

Therefore one side of square is 3√2

area of square = side * side = 3√2 * 3√2 = 18 square units

To find the area of triangle

The base of triangle = side of square = 3√2

base b = 3√2

Height of triangle is the diagonal of small square which is equal to √2

height h = 3√2

Area of triangle = bh/2  = (3√2 * √2)/2 = 6/2 = 3 square units

To find the total area

Total area = area of square + area of triangle = 18 = 3 = 21 square units.

x= 149. 24+7=31. 180-31=149

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