Trapezoid

Four Trapezia Formed by the Difference of Two Concentric Squares

Problem
ABCD is a square of side 10 cm. PQRS is a square inside ABCD. PQBA, QRCB, RSDC, and SPAD are identical trapezia, each of area 16 cm2. What is the height of each trapezium if PQ is parallel to AB and SR is parallel to DC?

A.   3 cm C.   2 cm
B.   1.8 cm D.   1.2 cm

 

2016-nov-math-trapezia_3d.jpg

02 Trapezoidal lot segregated from triangular land

Situation
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.
 

Part 1: Calculate the area of lot ABC.
A. 62,365 m2
B. 59,319 m2
C. 57,254 m2
D. 76.325 m2
 

Part 2: Calculate the area of lot ADE.
A. 8,342 m2
B. 14,475 m2
C. 6,569 m2
D. 11,546 m2
 

Part 3: Calculate the value of angle C
A. 57°
B. 42°
C. 63°
D. 68°
 

Length of one side for maximum area of trapezoid (solution by Calculus)

Problem
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.
 

Length of one side for maximum area of trapezoid (solution by Geometry)

Problem
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.
 

Common Quadrilaterals

Square

 
square.gif

 

Area, $A = a^2$

Perimeter, $P = 4a$

Diagonal, $d = a\sqrt{2}$

 

Trapezoidal Strip of Land from a Triangular Lot

Problem
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