# triangle

## 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°

## 715 Semicircle and Triangle | Centroid of Composite Figure

**Problem 715**

Determine the coordinates of the centroid of the area shown in Fig. P-715 with respect to the given axes.

## Derivation of Heron's / Hero's Formula for Area of Triangle

For a triangle of given three sides, say *a*, *b*, and *c*, the formula for the area is given by

where *s* is the semi perimeter equal to *P*/2 = (*a* + *b* + *c*)/2.

## 010 Components of force normal and tangent to hypotenuse of a triangle

**Problem 010**

The triangular block shown in Fig. P-010 is subjected to the loads P = 1600 lb and F = 600 lb. If AB = 8 in. and BC = 6 in., resolve each load into components normal and tangential to AC.

## 40 - Base angle of a growing right triangle

## 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