Question

Hi can I get help finding the area and perimeter of a shape

Answer 1

Given

AB=11yd

DA=8yd

Angle BCD = 72 degree

Angle CDA = 65 degree

Find

1. Area

2. Perimeter

Step-by-step explanation

Construction - draw a perpendicular from B to F and A to E

In triangle ADE

`\begin{gathered} sin65=(AE)/(8) \\ AE=8* sin65 \\ AE=7.25 \end{gathered}`

Now using the Pythogoras theorem to find x

`\begin{gathered} 8^2=x^2+7.25^2 \\ x^2=64-52.5625 \\ x=3.38 \end{gathered}`

Since AE=BF

So BF = 7.25

`\begin{gathered} sin72=(7.25)/(BC) \\ BC=7.623 \end{gathered}`

Using Pythogoras theorem to find y

`\begin{gathered} 7.623^2=7.25^2+y^2 \\ y=√(58.110129-52.5625) \\ y=2.35534\text{ yd} \end{gathered}`

Perimeter = AB+BC+CD+DA

11 + 7.623 + 11 + 3.38 + 2.35534 + 8 = 51.35834 yd

Area=

`\begin{gathered} A=(1)/(2)(sum\text{ }of\text{ }parrallel\text{ }sides)* height \\ =(1)/(2)(11+2.35534+3.38)*7.25 \\ =60.6656\text{ }yd^2 \end{gathered}`

Final Answer

Perimeter = 51.35834 yd

Area = 60.6656 yd square