# area of triangle

## 01 Area of a right triangle of known median bisecting the hypotenuse

**Problem**

The median of a right triangle drawn to the hypotenuse is 3 cm long and makes an angle of 60° with it. Find the area of the triangle.

A. 7.97 cm^{2} |
C. 8.79 cm^{2} |

B. 8.97 cm^{2} |
D. 7.79 cm^{2} |

## Length of hypotenuse of a right triangle of known area in the xy-plane

**Problem**

For triangle *BOA*, *B* is on the *y*-axis, *O* is the origin, and *A* is on the *x*-axis. Point *C*(5, 2) is on the line *AB*. Find the length of *AB* if the area of the triangle is 36 unit^{2}.

A. 24.31 units | C. 13.42 units |

B. 18.30 units | D. 10.80 units |

## 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°

## Solved Problem 13 | Rectangular Parallelepiped

**Problem 13**

The figure represents a rectangular parallelepiped; AD = 20 in., AB = 10 in., AE = 15 in.

(a) Find the number of degrees in the angles AFB, BFO, AFO, BOF, AOF, OFC.

(b) Find the area of each of the triangles ABO, BOF, AOF.

(c) Find the perpendicular distance from B to the plane AOF.

**Solution 13**

## Solved Problem 07 | Cube

## 06 Circular arcs inside and tangent to an equilateral triangle

**Example 06**

The figure shown below is an equilateral triangle of sides 20 cm. Three arcs are drawn inside the triangle. Each arc has center at one vertex and tangent to the opposite side. Find the area of region enclosed by these arcs. The required area is shaded as shown in the figure below.

## 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.