MENSURATION 



3736 



MENTAL HANDICAPS 



The area of a trapezoid is equal to that of a 

 rectangle whose base is one-half the sum of the 

 bases of the trapezoid, and whose altitude is the 

 same as that of the trapezoid. Put in another 

 form : To find the area of a trapezoid, multiply 

 one-half the sum of the bases by the altitude. 



1. Find the area of a trapezoidal piece of gold 

 leaf, one base 6 inches, the other base 4 inches 

 and the altitude 3 inches. 



Base =6 in. 

 Base =4 in. 



Average base=^y-i) in. = 5 in. 



Altitude = 3 in. 



Area in sq. in. = 3X5 = 15 



Draw this trapezoid. Make of it a rectangle 

 5 inches by 5 inches. 



2. A farmer has a field in the form of a trape- 

 zoid. The east boundary line is 40 rods; the 

 west boundary line, which is parallel to the 

 east line, is 60 rods. The distance between 

 these boundaries is 80 rods. How many acres 

 does the field contain? 



Base=60 rd. 

 Base =40 rd. 

 Altitude = 80 rd. 



Average base= 60 + 40 rd. = 50 rd. 



Number of acres = 



= 25 



General Problems in Surface. . 1. What is the 

 cost of plastering a room 16 feet by 14 feet, and 

 9 feet high, at $.50 per square yard? 



* 



Number ,. yd. in 

 = 



Number sq. yd. in ceiling= 

 Cost = 85x$. 50 = $42.50 



Allowance is made for openings in walls 'to 

 be plastered in some localities. Sometimes the 

 entire surface of the openings is deducted, 

 sometimes one-half the surface, and at times 

 no deduction is made. It is interesting and 

 good for the students and teacher to know the 

 local rules in matters of this kind. Always use 

 the nearest whole number of square yards; for 

 example, 12*4 is called 12, while 12% is 

 called 13. 



2. What will it cost to lay a concrete floor 

 in a milk house 54 feet long and 20 feet wide, 

 at $.95 per square yard? 



Number of sq. yd.= 



3. A roof is 30 feet long, 18 feet wide. If 9 

 shingles cover a square foot, and shingles sell at 

 $5 per thousand, what will the shingles for the 

 roof cost? 



Number of shingles needed = 30 X 18 X 9 = 4860 

 Cost=4.860X$5 = $24.30 

 Practical cost = 5 x $5 = $25. 00 



Shingles come in bunches of 250 each, and 

 one must purchase a bunch even though he 

 needs only a fraction of a bunch. 



4. A farm along the Illinois River consists 

 of a rectangular piece of land 1 mile long and 

 % mile wide, and a triangular piece with a 

 base of^/4 mile, and an altitude of % mile. 

 There is an assessment on the farm for drainage 

 of $52 per acre. What is the assessment? 



Area of rectangle in acres = 1X^X640 = 320 



Area of triangle in acres = ^ of ( % x Vz ) X 640 

 = 40 



Assessment = 360x$52 = $18720 



Note that the rectangular field contains y> a 

 square mile, and as there are 640 acres in 1 

 square mile, the field contains 1/2 of that, or 320 

 acres. The triangle contains i/ 2 the product of 

 its base and altitude, or V 2 of % square mile, or 

 Vie square mile, or 40 acres. 



Circle. For area of circle, see CIRCLE. In 

 connection with mensuration refer to and study 

 QUADRILATERAL; SQUARE; POLYGON; RHOMBUS; 

 TRIANGLE, and so on. Also see DENOMINATE 

 NUMBERS. 



Volumes. Some units for measuring volume 

 are the cubic inch, the cubic foot, the cubic 

 yard. The subject of volume measurements is 

 fully treated in these volumes in the article 

 CUBIC MEASURE. A.H. 



Related Subjects. A more detailed knowledge 

 of this subject in ' its various phases may be 

 gained from the following articles in these vol- 

 umes : 



Angle 



Area 



Arithmetic 



Circle 



Cone 



Cube 



Cube Root 



Cubic Measure 



Cylinder 



Geometry 



Polygon 



Prism 



Pyramid 



Quadrilateral 



Rectangle 



Rhombus 



Sphere 



Square 



Square Measure 



Trapezium 



Triangle 



Weights and Measures 



1 



= 120x$.95 = $114.00 



MENTAL HANDICAPS. Physical and men- 

 tal handicaps, or disorders, are always closely 

 related, for anything which interferes with the 

 health of the body is sure, directly or indi- 

 rectly, to influence the health of the mind. On 

 the other hand, many, if not most, mental dis- 

 orders react on the body. A truly sound mind 

 in an unsound body is hardly possible, although 

 it is of course true that occasionally a man or 



