Directions: Please find the area and side length of square ACEG. Please show all of your work (all of your calculation) in the grey box below.

9514 1404 393

Step-by-step explanation:

There are a couple of ways to do this. You can find the side length and then the area, or you can find the area and then the side length.

There are a couple of different ways to find the area. Here, we'll subtract the area of the triangles from the area of the larger square.

The larger square has sides of length 6+8 = 14, so its area is 14² = 196.

The area of each triangle is 1/2(6)(8) = 24, so the four of them together have a total area of 4×24 = 96.

Then the area of the smaller square is 196 -96 = 100 square units.

The side length is the square root of that, √100 = 10 units.

Alternate solution

Using the Pythagorean theorem, you can find the square of the side length (which is the area of the smaller square), and the side length.

  AC² = AB² +BC²

  AC² = 6² +8² = 36 +64 = 100 = area of ACEG

  AC = √100 = 10

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°