area of triangle

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

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 cm2 C.   8.79 cm2
B.   8.97 cm2 D.   7.79 cm2


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

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 unit2.

A.   24.31 units C.   13.42 units
B.   18.30 units D.   10.80 units


03 Point P Inside an Isosceles Right Triangle

Point P is inside the isosceles right triangle ABC. AP is 15 cm, BP is 9 cm and CP is 12 cm as shown. Determine the area of the triangle ABC.



02 Trapezoidal lot segregated from triangular land

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°

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.

Area, angle, and distance in rectangular parallelepiped.


Solution 13

Solved Problem 07 | Cube

Problem 07
Find the area of the triangle whose vertex is at the midpoint of an upper edge of a cube of edge a and whose base coincides with the diagonally opposite edge of the 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.

Circular arcs inside a triangle


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

$A = \sqrt{s(s - a)(s - b)(s - c)}$


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

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