Perimeter, Area, and Volume Geometry and andMeasurement

Measurement Rectangle Rectangle Perimeter Perimeter P = 2l + 2w, where l = length and w = width P = 2l + 2w, where l = length and w = width Example: l = 5 ft and w = 3 ft Example: l = 5 ft and w = 3 ft P rectangle =2l + 2w P rectangle =2l + 2w P=2(5 ft) + 2(3 ft) P=2(5 ft) + 2(3 ft) P=10 ft + 6 ft P=10 ft + 6 ft P=16 ft P=16 ft 3 ft 5 ft

Measurement Rectangle Rectangle Area Area A = lw where l = length and w = width A = lw where l = length and w = width Example: l = 5 ft and w = 3 ft Example: l = 5 ft and w = 3 ft A rectangle =lw A rectangle =lw A=(5 ft)(3 ft) A=(5 ft)(3 ft) A =15 ft 2 A =15 ft 2 3 ft 5 ft

Measurement Square Square Perimeter Perimeter P = 4s, where s = length of a side P = 4s, where s = length of a side Example: s = 3 ft Example: s = 3 ft P square =4s P square =4s P=4(3 ft) P=4(3 ft) P=12 ft P=12 ft 3 ft

Measurement Square Square Area Area A = s 2 where s = length of a side A = s 2 where s = length of a side Example: s = 3 ft Example: s = 3 ft A square =s 2 A square =s 2 A=(3 ft) 2 A=(3 ft) 2 A =9 ft 2 A =9 ft 2 3 ft

Measurement Triangle Triangle Perimeter Perimeter P = a + b + c, where a, b, and c are the lengths of the sides of the triangle P = a + b + c, where a, b, and c are the lengths of the sides of the triangle Example: a = 3 m; b = 4 m; c = 5 m Example: a = 3 m; b = 4 m; c = 5 m P triangle =a + b + c P triangle =a + b + c P=3 m + 4 m + 5 m P=3 m + 4 m + 5 m P=12 m P=12 m 3 m 5 m 4 m

Measurement Triangle Triangle Area Area A = ½ bh, where b is the base and h is the height of the triangle A = ½ bh, where b is the base and h is the height of the triangle Example: b = 3 m; h = 4 m Example: b = 3 m; h = 4 m A triangle =½ bh A triangle =½ bh A=½ (3 m) (4 m) A=½ (3 m) (4 m) A=6 m 2 A=6 m 2 3 m 5 m 4 m

Measurement Circle Circle Circumference Circumference C circle =  d or C = 2  r, where d = diameter and r = radius C circle =  d or C = 2  r, where d = diameter and r = radius Example: r = 3 cm Example: r = 3 cm C circle = 2  r C circle = 2  r C= 2  (3 cm) C= 2  (3 cm) C= 6  cm C= 6  cm 3 cm

Measurement Circle Circle Area Area A =  r 2, where r = radius A =  r 2, where r = radius Example: r = 3 cm Example: r = 3 cm A circle =  r 2 A circle =  r 2 A=  (3 cm) 2 A=  (3 cm) 2 A= 9  cm 2 A= 9  cm 2 3 cm

Measurement Rectangular Prism Rectangular Prism Volume: Volume: V = lwh where l is length; w is width; and h is height V = lwh where l is length; w is width; and h is height Example: l = 6 cm; w = 5 cm; h = 7 cm Example: l = 6 cm; w = 5 cm; h = 7 cm V rectangular prism = Bh = lwh V rectangular prism = Bh = lwh V=(6 cm)(5 cm)(7 cm) V=(6 cm)(5 cm)(7 cm) V=210 cm 3 V=210 cm 3 7 cm 6 cm 5 cm

Measurement Cube Cube Volume: Volume: V = s 3 where s is the length of a side V = s 3 where s is the length of a side Example: s = 5 cm Example: s = 5 cm V cube = Bh = s 3 V cube = Bh = s 3 V=(5 cm) 3 V=(5 cm) 3 V=125 cm 3 V=125 cm 3 5 cm

Measurement Triangular Prism Triangular Prism Volume: Volume: V = ½ bhl where b is the base; h is height of the triangle; and l is length of the prism V = ½ bhl where b is the base; h is height of the triangle; and l is length of the prism Example: b = 6 m; h = 5 m; l = 7 m Example: b = 6 m; h = 5 m; l = 7 m V triangular prism = Bh = ½ bhl V triangular prism = Bh = ½ bhl V=½ (6 m)(5 m)(7 m) V=½ (6 m)(5 m)(7 m) V=105 m 3 V=105 m 3 7 m 6 m 5 m

Measurement Cylinder Cylinder Volume of a Cylinder: V =  r 2 h where r is the radius of the base (circle) and h is the height. Volume of a Cylinder: V =  r 2 h where r is the radius of the base (circle) and h is the height. Example: r = 3 ft and h = 12 ft. Example: r = 3 ft and h = 12 ft. V cylinder =Bh =  r 2 h V cylinder =Bh =  r 2 h V=  (3 ft) 2  (12 ft) V=  (3 ft) 2  (12 ft) V=  (9 ft 2 )(12 ft) V=  (9 ft 2 )(12 ft) V=108  ft 3 V=108  ft 3 3 ft 12 ft

Measurement Cone Cone Volume: V =  r 2 h/3 where r is the radius of the base (circle) and h is the height. Volume: V =  r 2 h/3 where r is the radius of the base (circle) and h is the height. Example: r = 5 ft; h = 12 ft Example: r = 5 ft; h = 12 ft V cone =  r 2 h/3 V cone =  r 2 h/3 V = [  (5 ft) 2  12 ft ]/ 3 V = [  (5 ft) 2  12 ft ]/ 3 V =[(25  ft 2 )(12 ft)]/3 V =[(25  ft 2 )(12 ft)]/3 V=(25  ft 2 )(4 ft) V=(25  ft 2 )(4 ft) V= 100  ft 3 V= 100  ft 3 5 ft 13 ft 12 ft

Measurement Sphere Sphere Volume of a Sphere: V = (4/3)  r 3 where r is the radius Volume of a Sphere: V = (4/3)  r 3 where r is the radius Example: r = 6 mm Example: r = 6 mm V sphere =4  r 3 /3 V sphere =4  r 3 /3 V=[4  x (6 mm) 3 ]/3 V=[4  x (6 mm) 3 ]/3 V=[4  x 216 mm 3 ]/3 V=[4  x 216 mm 3 ]/3 V=[864  mm 3 ]/3 V=[864  mm 3 ]/3 V=288  mm 3 V=288  mm 3 6 mm

Measurement Triangular Pyramid Triangular Pyramid Square Pyramid Square Pyramid