Need Help?

Get in touch with us

bannerAd

Triangle Area Examples and Problem Sums

Sep 13, 2022
link

Key Concepts

• Solving constant speed problems.

• Solving unit price problems.

• Using an equation to represent unit rate problems.

  1. Classification of triangles by angles 
  1. Find the area of the triangle:  

Count squares in the triangle: 

Full squares =12 

parallel

Half squares =8 means =4 squares  

Area of the triangle =12 full squares + 8 half squares 

                                      =12 +4 

                                      =16 Square units 

  1. When the perpendicular distance between a pair of lines is the same throughout, it can be called parallel lines 

The altitude of a triangle is the perpendicular line segment drawn from the vertex to the opposite side of the triangle. 

parallel

Example 1: 

A parallelogram can be decomposed into two identical triangles. How you use the formula of area of parallelogram to find the area of triangle? 

  • Identical triangles have the same base and height, so they also have the same area 

Area of triangle =12 area of parallellogram

Area of triangle A=1/2 .bh Sq.units 

The area of one triangle is half the area of the related parallelogram. 

  • Area of parallelogram A=bh Sq.units 
  • Area of Triangle A= 1/2 of the area of parallelogram Sq.units 

Th area of triangle = 1/2 b.h Sq.units 

  1. Two identical triangles from a parallelogram with a base of 8 inches and height of 6 inches. What is the area of each triangle? Explain. 

A diagonal divides the parallelogram into two identical triangles with same base and height then the area of triangles are equal. 

Given that  

Base of the triangle = 8 in  

Height of the triangle=6 in 

Area of the triangle = ½ bh Sq.units                       

= 1/2 x 8 x 6 

=4 x 6 

= 24 

Area of each triangle is 24in2

Example 2: 

A = ½ bh 

 A = ½ x 8 x8  

     = 32  

The area of the side of the birdhouse is 32 square inches 

Example 3: 

Kaylan drew the triangle shown below. What is the area of triangle? 

Any side of a triangle can be its base. The height is the perpendicular distance from the base to the height of the opposite vertex 

One way 

A = ½ bh 

A=  ½ 10 x 8 

A= 40 

The area is 40 square feet. 

Another way 

A = ½ bh 

A= ½ 16 x 5 

A= 40 

The area is 40 square feet. 

Key concept:  

  1. Find the area of triangle 

Solution: 

Given that, 

height(h)= 2 ft 
base(b)= 4 ft 

Area of the triangle = 1/2xbh 

           = 1/2 x 4 x 2 

                = 4 square feet 

  1. Find the area of triangle 

Solution: 

Given that, 

height(h)=3.5 in 

base(b)=4.2 in 

Area of the triangle = ½bh 

           = ½  x 4.2 x 3.5 

           =7.35 square inches 

  1. find the area of triangle 

Solution:  

Given that, 

Height= 6.5 cm 

base = 5 cm 

Area of the triangle = ½ bh 

           = ½ x 5 x 6.5 

           = 2.5 x 6.5 

           = 16.25 

Area of the triangle is 16.25 square centimeters.  

Practice and problem solving: 

  1. The base of the triangle is 2ft. The height of the triangle is 15 in. find the area of the triangle in square inches? 

Given that, 

Height = 15 in 

base = 2ft 

          = 2 x 12     (∵1ft=12 in) 

          = 24 in 

Area of the triangle = ½ bh 

           = ½ 24 x 15 

           =  12 x 15 

           =  180 

 Area of the triangle is 16.25 square centimeters.  

  1. The dimensions of the sail for Erica’s sail boat are shown. Find the area of the sail?  

Given that , 

the dimensions of the sail are 

height = 15ft 

base   = 9ft 

Area of the sail = ½ bh 

   = ½ 9 x 15 

     = 9 x 7.5 

   = 67.5 

∴ Area of the sail is 67.5 ft2

Exercise:

1. The vertices of a triangle are A (0,0),B (3, 8) and C (9, 0). What is the area of this triangle?

2. If you know the area and the height of the triangle, how can you find the base?

3. Find the height and the base where the base is twice the height and the area is 49 ne

4. Find the area of the triangle if the base and height are 20 cm, 2 m respectively?

5. What is the formula for base when the height and area is given?

6. Find the area of the triangle where the base is 10 cm and the height is 20 cm?

7. Find the area of triangle with the base 25 cm and the height 25 cm?

8. Find the base of the triangle where the area is 2 cm2 and the height is 2 cm?

What have we learned?

• Solving constant speed problems.

• Solving unit price problems.

• Using an equation to represent unit rate problems.

Comments:

Related topics

Composite Figures – Area and Volume

A composite figure is made up of simple geometric shapes. It is a 2-dimensional figure of basic two-dimensional shapes such as squares, triangles, rectangles, circles, etc. There are various shapes whose areas are different from one another. Everything has an area they occupy, from the laptop to your book. To understand the dynamics of composite […]

Read More >>
special right triangles_01

Special Right Triangles: Types, Formulas, with Solved Examples.

Learn all about special right triangles- their types, formulas, and examples explained in detail for a better understanding. What are the shortcut ratios for the side lengths of special right triangles 30 60 90 and 45 45 90? How are these ratios related to the Pythagorean theorem?  Right Angle Triangles A triangle with a ninety-degree […]

Read More >>
simplify algebraic expressions

Ways to Simplify Algebraic Expressions

Simplify algebraic expressions in Mathematics is a collection of various numeric expressions that multiple philosophers and historians have brought down. Talking of algebra, this branch of mathematics deals with the oldest concepts of mathematical sciences, geometry, and number theory. It is one of the earliest branches in the history of mathematics. The study of mathematical […]

Read More >>
solve right triangles

How to Solve Right Triangles?

In this article, we’ll learn about how to Solve Right Triangles. But first, learn about the Triangles.  Triangles are made up of three line segments. These three segments meet to form three angles. The lengths of the sides and sizes of the angles are related to one another. If you know the size (length) of […]

Read More >>

Other topics