# Trapezoid

- Read more about Four Trapezia Formed by the Difference of Two Concentric Squares
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## 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 m^{2}.

Part 1: Calculate the area of lot ABC.

A. 62,365 m^{2}

B. 59,319 m^{2}

C. 57,254 m^{2}

D. 76.325 m^{2}

Part 2: Calculate the area of lot ADE.

A. 8,342 m^{2}

B. 14,475 m^{2}

C. 6,569 m^{2}

D. 11,546 m^{2}

Part 3: Calculate the value of angle C

A. 57°

B. 42°

C. 63°

D. 68°

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

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## 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.

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## Common Quadrilaterals

**Square**

Perimeter, $P = 4a$

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

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## Trapezoidal Strip of Land from a Triangular Lot

**Problem**

A strip of 640 m^{2} 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

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## 41 - 42 Maxima and Minima Problems Involving Trapezoidal Gutter

**Problem 41**

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?

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## 38 - 40 Solved problems in maxima and minima

**Problem 38**

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.

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