In Problem 39, if the strip is L in. wide, and the width across the top is T in. (T < L), what base width gives the maximum capacity?
From a strip of tin 14 inches a trapezoidal gutter is to be made by bending up the sides at an angle of 45°. Find the width of the base for greatest carrying capacity.
A cylindrical glass jar has a plastic top. If the plastic is half as expensive as glass, per unit area, find the most economical proportion of the jar.
A trapezoidal gutter is to be made from a strip of tin by bending up the edges. If the cross-section has the form shown in Fig. 38, what width across the top gives maximum carrying capacity?
Solve Ex. 39, if the strip is 11 inches wide and the base is 7 inches wide.
BC of trapezoid ABCD is tangent at any point on circular arc DE whose center is O. Find the length of BC so that the area of ABCD is maximum.
A strip of 640 m2 is sold from a triangular field whose sides are 96 m, 72 m, and 80 m. The strip is of uniform width h and has one of its sides parallel to the longest side of the field. Find the width of the strip.
A. 7.1 m
B. 8.1 m
C. 8.7 m
D. 7.7 m
A triangular lot ABC have side BC = 400 m and angle B = 50°. The lot is to be segregated by a dividing line DE parallel to BC and 150 m long. The area of segment BCDE is 50,977.4 m2.
: Calculate the area of lot ABC.
A. 62,365 m2
B. 59,319 m2
C. 57,254 m2
D. 76.325 m2
: Calculate the area of lot ADE.
A. 8,342 m2
B. 14,475 m2
C. 6,569 m2
D. 11,546 m2
: Calculate the value of angle C
Quadrilateral is a polygon of four sides and four vertices. It is also called tetragon and quadrangle. For triangles, the sum of the interior angles is 180°, for quadrilaterals the sum of the interior angles is always equal to 360°
Classifications of Quadrilaterals
There are two broad classifications of quadrilaterals; simple and complex. The sides of simple quadrilaterals do not cross each other while two sides of complex quadrilaterals cross each other.
Simple quadrilaterals are further classified into two: convex and concave. Convex if none of the sides pass through the quadrilateral when prolonged while concave if the prolongation of any one side will pass inside the quadrilateral.
The following formulas are applicable only to convex quadrilaterals.