Id really appreciate u if u answer this for em

For the parallelogram ABCD the extensions of the angle bisectors AG and BH intersect at point P. Find the area of the parallelog

natita [175]

Answer:

The area of a parallelogram is 360 in.²

Step-by-step explanation:

Where DG = GH

GP = 12 in.

AB = 39 in.

∠DAB + ∠ABC = 180° (Adjacent angles of a parallelogram)

Whereby ∠DAB is bisected by AG and ∠ABC is bisected by BH

Therefore, ∠GAB + ∠HBA = 90°

Hence, ∠BPA = 90° (Sum of interior angles of a triangle)

$cos(\angle GAB) = \dfrac{AP}{AB} = \dfrac{AP}{39} = \dfrac{GP}{GH} =\dfrac{12}{GH}$

We note that ∠AGD = ∠GAB (Alternate angles of parallel lines)

∴ ∠AGD = ∠AGD since ∠AGD = ∠GAB (Bisected angle)

Hence AD = DG (Side length of isosceles triangle)

The bisector of ∠ADG is parallel to BH and will bisect AG at point Q

Hence ΔDAQ ≅ ΔDGQ ≅ ΔGPH and AQ = QG = GP

Hence, AP = 3 × GP = 3 × 12 = 36

$cos(\angle GAB) = \dfrac{AP}{AB} = \dfrac{36}{39}$

$\angle GAB = cos^{-1} \left (\dfrac{36}{39} \right )$

∠GAB = 22.62°

$cos(\angle GAB) = \dfrac{36}{39} = \dfrac{12}{GH}$

$GH = \dfrac{39}{36} \times {12}$

GH = 13 in.

∴ AD 13 in.

BP = 39 × sin(22.62°) = 15 in.

GH = √(GP² + HP²)

∠DAB = 2 × 22.62° = 45.24°

The height of the parallelogram = AD × sin(∠DAB) = 13 × sin(45.24°)

The height of the parallelogram = 120/13 = 9.23 in.

The area of a parallelogram = Base × Height = (120/13) × 39 = 360 in.²

7 0

3 years ago

Read 2 more answers

A nationwide survey of 100 boys and 50 girls in the first grade found that the daily average number of boys who are absent from

dusya [7]

Te difference of 2 standard deviation of a population n1 & n2 is given by the formula:
sigma (difference)=√(sigma1/n1 + sigma2/n2), Plug:

sigma(d)= √(49/100 + 36/50)

Sigma(d=difference) =1.1

6 0

4 years ago

Read 2 more answers

Construye un rectángulo de 12 cm de altura y 5 cm de ancho (Píntalo). Luego a) Calcula el perímetro del rectángulo. B) Calcula e

lara [203]

Step-by-step explanation:

Build a rectangle 12 cm high and 5 cm wide (Paint it). Then a) Find the perimeter of the rectangle. B) Find the area of the rectangle. Aiuda porfis.

Length of the rectangle is 12 cm

Breadth of the rectangle is 5 cm

Perimeter is the sum of all sides. For rectangle it is given by :

P = 2(l+b)

⇒ P=2(12+5)

P = 34 cm

Area of a rectangle is equal to the product of its length and breadth.

So,

A = lb

A = 12 cm × 5 cm

⇒A = 60 cm²

Hence, perimeter is 34 cm and area of rectangle is 60 cm².

8 0

4 years ago

What’s the solution for x-0= 0

Dominik [7]

I’m pretty sure it’s 0

7 0

3 years ago

Pls help me with this question and explain how you got the answer!!!!!

Luba_88 [7]

Answer:

-87

Step-by-step explanation:

So, first to find x you need to subtract 121 from 180. You do this because both the angle which measures 121 degrees and x lie on the same line, and since a line has an angle measure of 180, you do 180-121 to find x. The same thing can be done for y. Since the angle measure of 34 degrees and y lie on the same line you can calculate 180-34 to get y. So, let's do that.

180-121=x

59=x

180-34=y

146=y

Once you've done that you can easily subtract the two and get your answer.

x-y

substitute the answer for the variables and get

59-146

and then your answer is

-87

4 0

3 years ago