Triangle - Examples, Exercises and Solutions

Understanding Triangle

Complete explanation with examples

Geometric shapes

There is a wide variety of geometric shapes, which you can read about in detail:

Triangle

Rectangle

Trapezoid

Parallelogram

kite

Rhombus

Diagram displaying eight geometric shapes: Triangle, Square, Rectangle, Circle, Parallelogram, Trapezoid, Rhombus, and Kite. Each shape is labeled in English beneath it.

Detailed explanation

Practice Triangle

Test your knowledge with 48 quizzes

Given the parallelogram of the figure

What is your area?

999555AAABBBCCCDDDEEE

Examples with solutions for Triangle

Step-by-step solutions included
Exercise #1

ABDC is a deltoid.

AB = BD

DC = CA

AD = 12 cm

CB = 16 cm

Calculate the area of the deltoid.

161616121212CCCAAABBBDDD

Step-by-Step Solution

First, let's recall the formula for the area of a rhombus:

(Diagonal 1 * Diagonal 2) divided by 2

Now we will substitute the known data into the formula, giving us the answer:

(12*16)/2
192/2=
96

Answer:

96 cm²

Video Solution
Exercise #2

The trapezoid ABCD is shown below.

AB = 2.5 cm

DC = 4 cm

Height (h) = 6 cm

Calculate the area of the trapezoid.

2.52.52.5444h=6h=6h=6AAABBBCCCDDD

Step-by-Step Solution

First, let's remind ourselves of the formula for the area of a trapezoid:

A=(Base + Base) h2 A=\frac{\left(Base\text{ }+\text{ Base}\right)\text{ h}}{2}

We substitute the given values into the formula:

(2.5+4)*6 =
6.5*6=
39/2 = 
19.5

Answer:

1912 19\frac{1}{2}

Video Solution
Exercise #3

The trapezoid ABCD is shown below.

Base AB = 6 cm

Base DC = 10 cm

Height (h) = 5 cm

Calculate the area of the trapezoid.

666101010h=5h=5h=5AAABBBCCCDDD

Step-by-Step Solution

First, we need to remind ourselves of how to work out the area of a trapezoid:

Formula for calculating trapezoid area

Now let's substitute the given data into the formula:

(10+6)*5 =
2

Let's start with the upper part of the equation:

16*5 = 80

80/2 = 40

Answer:

40 cm²

Video Solution
Exercise #4

Shown below is the deltoid ABCD.

The diagonal AC is 8 cm long.

The area of the deltoid is 32 cm².

Calculate the diagonal DB.

S=32S=32S=32888AAABBBCCCDDD

Step-by-Step Solution

First, we recall the formula for the area of a kite: multiply the lengths of the diagonals by each other and divide the product by 2.

We substitute the known data into the formula:

 8DB2=32 \frac{8\cdot DB}{2}=32

We reduce the 8 and the 2:

4DB=32 4DB=32

Divide by 4

DB=8 DB=8

Answer:

8 cm

Video Solution
Exercise #5

Given the trapezoid:

999121212555AAABBBCCCDDDEEE

What is the area?

Step-by-Step Solution

Formula for the area of a trapezoid:

(base+base)2×altura \frac{(base+base)}{2}\times altura

We substitute the data into the formula and solve:

9+122×5=212×5=1052=52.5 \frac{9+12}{2}\times5=\frac{21}{2}\times5=\frac{105}{2}=52.5

Answer:

52.5

Video Solution

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