FIND THE AREA FOR BOTH SHAPES (LEAVE EXPLANATION)

b - 100 cm²

c - 45.5 cm²

Step-by-step explanation:

Hello There!

For b - The following figure shown is a trapezoid with the dimensions

height = 10cm

longer base = 12cm

shorter base = 8cm

We can calculate the area of a trapezoid using this formula

where a and b are bases and h = height

knowing the dimensions all we have to do is plug in the values

so we can conclude that the area of figure b is 100 cm²

for a

The figure shown is an irregular shape so to calculate the area we're going to want to divide the irregular shape into two regular shapes

a rectangle with the dimensions:

width = 7 cm

length = 8cm (total height of irregular figure) - 3cm (height of the triangle)

8cm-3cm=5cm so the length of the rectangle is 5cm

a triangle with the dimensions:

base (length) = 7cm

height = 3cm

Now lets find the area of each shape

for the rectangle:

the area of a rectangle can simply be found by multiplying the length and width

7 * 5 = 35 so the area of the rectangle is 35 cm²

for the triangle:

the area of a triangle can be found using this formula

where b = base and h = height

knowing the dimensions all we have to do is plug in the values

so we can conclude that the area of the triangle is 10.5 cm²

finally we add the two areas of the regular shapes

10.5 + 35 = 45.5 cm²

In conclusion the area of the figure is 45.5 cm²

g(x) = x² + 2

step-by-step explanation:

it is given that the graphs are the same shape.

the only difference is that the red graph is 2 units higher than the blue graph.

that is to say that the red graph is simply the blue graph that has been moved vertically by 2 units in the positive y direction.

hence

g(x) = f(x) + 2

or

g(x) = x² + 2

the answer is b.

step-by-step explanation:

by the trigonometric ratio tangent, tangent equals opposite divided by adjacent.

therefore, tan(50) equals ac/3

multiply each side by 3 to get: ac=3tan(50)

the answer is b.