Chapter 8 Area Flashcards
Area of a rectangle
A=lw
Area of a parallelogram
A=bh
Area of a triangle
A=1/2bh
Area of a trapezoid
A=1/2(b1+b2)h
A= m*h (median is (b1+b2)/2)
Area of a Kite/Rhombus
A=1/2(d1*d2)
Are of a Regular Polygon
A=1/2ap
Area of a Circle
A=(Pi)r^2
Area of a sector
As=x°/360°*(Pi)r^2
Area of a square
A=s^2
Or
A=d^2/2
Area of a segment
Asg=As-At
Asg=x°/360°*(Pi)r^2-1/2bh
Area of an annulus
A=(Pi)R^2*(Pi)r^2
Area of the big circle minus the area of the little circle
Lateral Area
LA=ph
Ex. Rectangular prism with a height of 15, and base edges with the length of 5 and 16.
LA=ph. LA=(5+5+16+16)15. LA=(42)15. LA=630u^2
Total Area
Ex. Rectangular prism with a height of 15, and base edges with the length of 5 and 16. LA=630u^2
TA=LA+2B (B is the area of the base. In this case a rectangle)
TA=630+2(5*16). TA= 630+2(80). TA=630+160. TA=790u^2
Lateral area of a pyramid
LA=1/2p(L) L is the slant height
Ex. A square pyramid with a slant height of 26 and base edges of 20.
LA=1/2(20+20+20+20)26. LA=1/2(80)26. LA=(40)26. LA=1040u^2
Total area for a pyramid
TA=LA+B (only one base because a pyramid only has one base)
Ex. A square pyramid with a slant height of 26 and base edges of 20. The lateral area is 1040u^2.
TA=1040+(s^2). TA=1040+(20^2). TA=1040+400. TA=1440u^2.
Lateral Area for a cylinder
LA=2(Pi)rh
Ex. A cylinder with a radius of 4 and a height of 7.
LA=2Pi(4)7. LA=8Pi(7). LA=56Pi
Total area of a cylinder
TA= LA+2(Pi)r^2
Ex. A cylinder with a radius of 4 and a height of 7. LA=56Pi
TA=56Pi+2Pi(4)^2. TA=56Pi+2(16Pi). TA=56Pi+32Pi. TA=88Pi
Lateral area of a cone
LA=(Pi)r(L) (L is the slant height)
Ex. A cone has a slant height of 30 and a radius of 13.
LA=Pi(13)(30). LA=390Pi
Total area of a cone
TA= LA+(Pi)r^2
Ex. A cone has a slant height of 30 and a radius of 13. LA=390Pi
TA=390Pi+Pi(13)^2. TA=390Pi+Pi(169). TA= 559(Pi)u^2
Area of a sphere
A=4(Pi)r^2
Area of a hemisphere
A=2(Pi)r^2
