12 Free Area of a Triangle Worksheets | 80+ Area Problems
Our area of a triangle worksheet is designed to make learning geometry enjoyable and educational for young minds. Try out these triangle activities by practicing the area of a triangle worksheet.
7 Diverse Types to Calculate Area of a Triangle
Here, we have 10+ free area of a triangle worksheet for the integer, fraction, and decimal-type problems.
Introduction to the Area of a Triangle
The area of a triangle means the space enclosed by the boundary of the triangle.
There are different types of triangles like equilateral triangles, right angle triangles, isosceles triangles, and scalene triangles.
The area of a triangle is ½ x base x height. The equation of the area of a triangle is different when the shape is different. Look at the below image very carefully.
We have shown other areas of different types of triangles.
Area of Right Angle Triangle
When there is an angle of 90° in a triangle it is called the right angle triangle. The area of the triangle will be,
Area = ½ x b x h
Problem: A right-angle triangle has a base of 5 m and a height is 3 m. What is the area of this triangle?
Solution:
Area = ½ x b x h
= ½ x 5 x 3 m²
See the below image for better visualization.
Integer Type
This is a PDF of the area of a triangle worksheet. The problems are given in the integer form. Use a calculator while practicing them.
Decimal Type
Here is the PDF of the area of a triangle worksheet for decimal types. Write the answer to two decimal places.
Fraction Type
There are practice problems of fraction type length of this area of a triangle worksheet. Practice them and leave the answers in fraction form.
Area of Equilateral Triangle
The equilateral triangle means where the three sides are equal and the angles are also equal.
The area of the equilateral triangle is,
Area = √3/4 a²
Here, “a” is the common side of the triangle.
Problem: An equilateral triangle has a side of 8 in. Find the area of this triangle.
Solution:
Area = √3/4 a²
= √3/4 x (8)²
= 27.712 in²
We have attached a problem here for your better understanding.
Integer Type
This is the PDF of the area of a triangle worksheet for the integer type.
Decimal Type
Here is the PDF for the area of a triangle worksheet of decimal values. The sides are displayed in the decimal form in this worksheet. Write the answer of the area to two decimal places.
Area of Isosceles Triangle
The isosceles triangle is where the two arms are equal and the other is not. The area of an isosceles triangle is
Area = b/4 √(4a²-b²)
Suppose, an isosceles triangle has equal arms of 10 ft and the other arm is 8 ft. Then what will be the area?
The problem is simple. We need to write the area’s equation first.
Area = b/4 √(4a²-b²)
= (8/4) x √(4×10²-8²) ft²
= 36.66 ft²
The below image will clear up your confusion.
Integer Type
This area of a triangle worksheet contains integer types problems. Download the PDF to become a master of this type of skill.
Decimal Type
Here is the PDF of the area of a triangle worksheet of decimal types.
Area of Scalene Triangle
The scalene triangle is a triangle where all the sides are unequal. For this type of triangle, you need to find half of the perimeter first.
Semi-perimeter, s = (a + b + c)/2
Then the area will be,
Area = √{s x (s-a) x (s-b) x (s-c)
Where, a,b, and c are the three sides of the triangle and “s” is the semi-perimeter.
Problem: A triangle has three sides of 5 cm, 7 cm, and 10 cm. What will be the area of the triangle?
Solution:
The semi-perimeter = ( 5 + 7 + 10)/2
= 11 cm
Area = √{s x (s-a) x (s-b) x (s-c)}
= √ 11 x (11- 5) x (11-7) x ( 11-10) cm²
= √11 x 6 x 4 x 1 cm²
= √264 cm²
= 16.25 cm²
Integer Type
We have given some practice problems of integer types in this area of a triangle worksheet. Practice them and have fun!
Decimal Type
Practice these decimal types of problems in the area of a triangle worksheet.
Finding Area of a Triangle with Angle Problems
We have discussed the methods for particular types of triangles. But if you want to estimate the area of a triangle where the angle between two adjacent sides is given. The area will be,
Area = ½ x bc x sinA
Where A is the angle between two adjacent sides b and c.
Problem: A triangle has two arms of 3 m and 2 m and the angle between these two is 30°. Find the area of this triangle.
Solution:
Area = ½ x bc x sin A
= ½ x 3 x 2 x sin 30° m²
= 1.5 m²
Now, it’s time for your practice. This PDF of the area of a triangle worksheet contains some triangles whose angles and two adjacent arms are given.
Unit Conversion Problems to Calculate the Area of a Triangle
You need to convert the units in the given format.
Suppose you have a triangle whose base is 5 m and the height is 400 cm. What will be the area of this triangle in cm²?
Solution:
Base = 5 m
= 500 cm
Height = 400 cm
Area = ½ x 500 x 400
= 100000 cm²
Here is the PDF of the area of a triangle worksheet where the units are
Word Problem for Finding the Area of a Triangle
This is the area of a triangle worksheet for word problems. Various kinds of word problems are inserted here. Practice the PDF of the area of a triangle worksheet.
Download Practice Worksheet PDF
This is the combined form of all the workheets.
You may also like these area of triangle worksheets.
So, these are the PDFs of the area of a triangle worksheet. We tried our best to insert 80+ practice problems for different types of triangles. Please, download the free printable PDF of the area of a triangle worksheet and give them to the students for practice.
