Solved Examples on Obtuse-Angled Triangle

Example 1: Calculate the area of an obtuse triangle whose height is 8 cm and the base is 6 cm.

Solution:

Given,

Height of Triangle (h) = 8 cm

Base of Triangle (b) = 6 cm

We know that,

Area of the triangle (A) = ½ × b × h

⇒ A = ½ × 6 × 8

⇒ A = ½ × 48

⇒ A = 24 sq. cm.

Hence, the area of the given obtuse triangle is 24 sq. cm.

Example 2: What is the area of an obtuse triangle whose sides are AB = 14 cm, BC = 9 cm, and AC = 7 cm?

Solution:

Given,

Sides of Obtuse Triangle are,

AB = c = 14 cm
BC = a = 9 cm
AC = b = 7 cm

We know that,

Area of Triangle =

and s = (a+b+c)/2
⇒ s = (14+9+7)/2
⇒ s = 30/2 = 15

Thus, A =

⇒

⇒ A = √720 sq. cm

⇒ A = 26.833 sq. cm

Hence, the area of the given obtuse triangle is 26.833 sq. cm.

Example 3: Check if the angles 95°, 40°, and 45° constitute an Obtuse Angled Triangle.

Solution:

We know that in an Obtuse-Angled Triangle an angle greater than 90° must exist.

Here,

One Angle of triangle = 95° > 90°

Also,

95° + 40 + 45° = 180°

The Sum of all angles of triangle is 180°, i.e. this triangle follow angle sum property of traingle.

Thus, the given traingle is an Obtuse Angled Triangle.

Example 4: What is the perimeter of an obtuse triangle PQR whose sides are PQ = 12 units, QR = 10 units, and PR = 6 units?

Solution:

Given.

Sides of Obtuse Triangle
PQ = r = 12 units
QR = p = 10 units
PR = q = 6 units

Perimeter of Obtuse Triangle (P) = p + q + r

⇒ P = (10 + 6 + 12) units

⇒ P = 28 units

Hence, the perimeter of the obtuse triangle is 28 units.

Obtuse Angled Triangle

Obtuse angle triangles are triangles in which one angle of the triangle measures greater than 90 degrees. As the name suggests one angle of an obtuse angle triangle is an obtuse angle. A triangle is a closed, two-dimensional geometric figure with three angles, and the sum of all the angles of a triangle is 180 degrees. On the basis of a measure of angles, we divide the triangle into three categories i.e.

Now, let’s learn more about obtuse angled triangles, their properties, formulas, examples, and others in detail in this article.

Solved Examples on Obtuse-Angled Triangle

Obtuse Angled Triangle

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