Find the area of the following shape. You must show all work to receive credit.

51.5 square units

Step-by-step explanation:

To find the area of an irregular shape, one method that can be used is to divide the area into simple shapes. Then you calculate the area of each simple shape using a known formula. Finally, you add all the areas together.

Let's divide the area into 2 trapezoids and 1 triangle.

First trapezoid at the bottom:

Draw a segment from point F to (11, -6), which is 2 units above B.

Below this segment, there is a trapezoid with base lengths: 11 and 6, and height 2.

Area of first trapezoid = (b1 + b2)h/2 = (11 + 6)(2)/2 = 17

Second trapezoid in the middle:

Draw a segment from point E through point D and ending at point (11, -3).

Below this segment, there is a trapezoid with base lengths: 11 and 7, and height 3.

Area of second trapezoid = (b1 + b2)h/2 = (11 + 7)(3)/2 = 27

Triangle on top:

The segment from point D to point (11, -3) is the bottom side of a triangle whose base is 5 and whose height is 3.

Area of triangle = bh/2 = (5)(3)/2 = 7.5

Total Area = Area of first trapezoid + area of second trapezoid + area of triangle

Total Area = 17 + 27 + 7.5

Total Area = 51.5

answer:

the position of equilibrium will shift to the left.

step-by-step explanation:

the general equation for the dissociation of a weak base is

b + h₂o   ⇌   bh⁺ + oh⁻

according to le châtelier's principle, when a stress is applied to a system at equilibrium, the system will respond in a way that tends to relieve the stress.

if you apply a stress by adding more bh⁺ or oh⁻,   the system will respond by moving in a direction that gets rid of the added ions.

the position of equilibrium will shift to the left, forming more of the undissociated base.

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°