Answer:
12. 1144.8668 (round if needed) 13. 52.5
Step-by-step explanation:
Area of a triangle: [tex]A =[/tex] [tex]\frac{1}{2}[/tex] x [tex]b[/tex] x [tex]h[/tex]
Area of a rectangle: [tex]A =[/tex] [tex]w[/tex] x [tex]h[/tex]
[tex]A =[/tex] area [tex]b =[/tex] base [tex]h =[/tex] height [tex]w =[/tex] width
12. Inside of the rectangle are two triangles. Use the pythagorean theorem to find the height of the triangles.
[tex]a^{2} +b^{2} =c^{2}[/tex]
Substitute [tex]32[/tex] for [tex]b[/tex] and [tex]48[/tex] for [tex]c[/tex]
[tex]a^{2}+32^{2}=48^{2}[/tex]
Square the numbers
[tex]a^{2}+1024=2304[/tex]
Subtract [tex]1024[/tex] from each side
[tex]a^{2}=1280[/tex]
Take the square root from each side
[tex]a = 35.777[/tex]
[tex]a[/tex] is the measurement of the height [tex]h[/tex]
Use the formula to find the area of the rectangle
[tex]A =[/tex] [tex]w[/tex] x [tex]h[/tex]
Substitute [tex]32[/tex] for [tex]w[/tex] and [tex]35.777[/tex] for h
[tex]A =[/tex] [tex]32[/tex] x [tex]35.777[/tex]
Solve
[tex]A = 1144.8668[/tex]
Round if needed
13. This is an irregular polygon. Separate the the shape into regular polygons. A triangle and a rectangle.
Use the formula to find the area of the triangle.
[tex]A =[/tex] [tex]\frac{1}{2}[/tex] x [tex]b[/tex] x [tex]h[/tex]
Substitute [tex]15[/tex] for [tex]b[/tex] and [tex]1[/tex] for [tex]h[/tex]
[tex]A =[/tex] [tex]\frac{1}{2}[/tex] x [tex]15[/tex] x [tex]1[/tex]
Solve
[tex]A =[/tex] [tex]7.5[/tex]
Use the formula to find the area of the rectangle.
[tex]A = w[/tex] x [tex]h[/tex]
Substitute [tex]15[/tex] for [tex]w[/tex] and [tex]3[/tex] for [tex]h[/tex]
[tex]A =[/tex] [tex]15[/tex] x [tex]3[/tex]
Solve
[tex]A = 45[/tex]
Add the two areas together to get the total area of the irregular polygon
[tex]A = 7.5 + 45[/tex]
Solve
[tex]A = 52.5[/tex]
