Question

Find the area and perimeter of the paper airplane shape.

Answer 1

Step-by-step explanation

Geometry / Triangles Area and Perimeter

In this problem, we have a diagram of a paper airplane, and we must compute its area and perimeter.

The area of a triangle with height h and base b is:

`A=√(s\cdot(s-a)\cdot(s-b)\cdot(s-c)).`

Where:

• a, b and c are the lengths of the sides of the triangle,

,

• s is the semi perimeter, which is given by:

`s=(a+b+c)/(2).`

(1) The area of the airplane is given by:

`A=A_b-A_s.`

Where:

• Ab is the area of the bigger triangle,

,

• As is the area of the smaller triangle.

Bigger triangle

The bigger triangle has sides a = b = 5 cm and c = 4 cm, is semi perimeter is given by:

`s=(5cm+5cm+4cm)/(2)=7cm.`

The area of the bigger triangle is:

`A_b=√(7cm\cdot(7cm-5cm)\cdot(7cm-5cm)\cdot(7cm-4cm))=2√(21)\text{ }cm^2.`

Smaller triangle

The smaller triangle has sides a = b = 3 cm and c = 4 cm, is semi perimeter is given by:

`s=(3cm+3cm+4cm)/(2)=5cm.`

The area of the smaller triangle is:

`A_s=√(5cm\cdot(5cm-3cm)\cdot(5cm-3cm)\cdot(5cm-4cm))=2√(5)\text{ }cm^2.`

Replacing these results in the formula for the area of the airplane, we get:

`A=2√(21)\text{ }cm^2-2√(5)\text{ }cm^2=2(√(21)-√(5))\text{ }cm^2\cong4.69\text{ }cm^2.`

(2) The perimeter of the airplane is the sum of the length of the sides:

`P=5cm+5cm+3cm+3cm=16cm.`Answer

The area and perimeter of the airplane are:

`\begin{gathered} A=2(√(21)-√(5))\cong4.61cm^2, \\ P=16\text{ }cm. \end{gathered}`