Question

trying it out #8: perimeter and area of the composite figure. use the shapes on the left side to break the composite figure into smaller polygons. resize them as needed. area: sq. units my math.... perimeter: units my math....

Explanation:

Step1: Calculate the area of the rectangle

The rectangle has length 8 and width 6. The area of a rectangle is $A = l\times w$, so $A_{rectangle}=8\times6 = 48$ square - units.

Step2: Calculate the area of the triangle

The base of the triangle is $11 - 8=3$ and the height is 6. The area of a triangle is $A=\frac{1}{2}\times b\times h$, so $A_{triangle}=\frac{1}{2}\times3\times6 = 9$ square - units.

Step3: Calculate the total area

The area of the composite figure is the sum of the area of the rectangle and the area of the triangle. $A = A_{rectangle}+A_{triangle}=48 + 9=57$ square - units.

Step4: Calculate the lengths of the non - straight sides

Using the Pythagorean theorem for the non - vertical and non - horizontal sides. For the slanted side of the triangle with base 3 and height 6, $c=\sqrt{3^{2}+6^{2}}=\sqrt{9 + 36}=\sqrt{45}=3\sqrt{5}$. There are two such slanted sides.

Step5: Calculate the perimeter

The perimeter of the composite figure is $P=11 + 6+3\sqrt{5}+3\sqrt{5}+8=25 + 6\sqrt{5}\approx25+6\times2.24=25 + 13.44 = 38.44$ units.

Answer:

Area: 57 sq. units
Perimeter: $25 + 6\sqrt{5}\approx38.44$ units