Given the parallelogram of the figure What is your area? 9 9 9 5 5 5 A A A B B B C C C D D D E E E

It is not possible to calculate

Triangle Practice Problems: Types, Properties & Geometry

Master triangle types, angle calculations, and geometric properties with interactive practice problems. Build confidence in equilateral, isosceles, right, and scalene triangles.

📚What You'll Master in Triangle Practice

Identify and classify equilateral, isosceles, right, and scalene triangles
Calculate missing angles using the 180-degree angle sum property
Apply Pythagorean theorem to solve right triangle problems
Recognize special properties of each triangle type
Solve real-world problems involving triangle measurements
Understand relationships between sides, angles, and triangle classification

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

Detailed explanation

Practice Triangle

Test your knowledge with 48 quizzes

Look at the deltoid in the figure:

What is its area?

Examples with solutions for Triangle

Step-by-step solutions included

Exercise #1

ACBD is a deltoid.

AD = AB

CA = CB

Given in cm:

AB = 6

CD = 10

Calculate the area of the deltoid.

Step-by-Step Solution

To solve the exercise, we first need to remember how to calculate the area of a rhombus:

(diagonal * diagonal) divided by 2

Let's plug in the data we have from the question

10*6=60

60/2=30

And that's the solution!

Answer:

Video Solution

Exercise #2

ABDC is a deltoid.

AB = BD

DC = CA

AD = 12 cm

CB = 16 cm

Calculate the area of the deltoid.

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 #3

Look at the kite ABCD below.

Diagonal DB = 10

CB = 4

Is it possible to calculate the area of the kite? If so, what is it?

Step-by-Step Solution

To determine if we can calculate the area of the kite, let's consider the steps we would use given complete data:
To calculate the area of a kite, we typically use the formula:

\text{Area} = \frac{1}{2} \times d_1 \times d_2

where $d_1$ and $d_2$ represent the lengths of the kite's diagonals.

In this case:

We are given that diagonal $DB = d_1 = 10$ cm.
However, we lack the length of the other diagonal, $AC = d_2$ .

Without knowing $AC$ , we cannot apply the formula to calculate the area. Thus, given the information provided, it is not possible to determine the area of the kite.

Therefore, the solution to the problem is: It is not possible.

Answer:

It is not possible.

Video Solution

Exercise #4

Given the parallelogram of the figure

What is your area?

Step-by-Step Solution

To find the area of the parallelogram, we will use the formula:

A = \text{base} \times \text{height}

From the problem, we identify the base as $7 \, \text{cm}$ and the height as $4 \, \text{cm}$ . Substituting these values into the formula, we get:

A = 7 \, \text{cm} \times 4 \, \text{cm} = 28 \, \text{cm}^2

Therefore, the area of the parallelogram is $28 \, \text{cm}^2$ .

Answer:

$28\operatorname{cm}^2$

Video Solution

Exercise #5

Below is the parallelogram ABCD.

AEC = 90°

What is the area of the parallelogram?

Step-by-Step Solution

To find the area of parallelogram ABCD, we will follow these steps:

Step 1: Identify the base and height from the given diagram.
Step 2: Apply the area formula for the parallelogram.
Step 3: Calculate the area using the identified base and height.

Let's execute these steps:

Step 1: In parallelogram ABCD, the length of side CD is given as 11 cm. Since angle AEC is a right angle, AE, which measures 9 cm, serves as the height of the parallelogram.

Step 2: Use the formula for the area of a parallelogram:
$\text{Area} = \text{base} \times \text{height}$

Step 3: Substitute the values into the formula:
$\text{Area} = 11 \, \text{cm} \times 9 \, \text{cm} = 99 \, \text{cm}^2$

Thus, the area of the parallelogram ABCD is $\mathbf{99 \, \text{cm}^2}$ .

Answer:

$99$ cm².

Video Solution

Frequently Asked Questions

Everything you need to know about Triangle

What are the 4 main types of triangles and their properties?

The four main types are: 1) Equilateral - all sides and angles equal (60° each), 2) Isosceles - two equal sides and two equal base angles, 3) Right - one 90° angle with two legs and a hypotenuse, 4) Scalene - all sides and angles different from each other.

How do you find a missing angle in any triangle?

Use the triangle angle sum property: all angles in a triangle add up to 180°. If you know two angles, subtract their sum from 180° to find the third angle. For example, if two angles are 60° and 80°, the third angle is 180° - 60° - 80° = 40°.

What makes a right triangle special compared to other triangles?

A right triangle has one 90° angle formed by two perpendicular sides called legs. The side opposite the right angle is the hypotenuse (longest side). Right triangles follow the Pythagorean theorem: a² + b² = c², where c is the hypotenuse.

How can you tell if a triangle is isosceles just by looking at it?

An isosceles triangle has two equal sides (legs) and two equal base angles. The height from the vertex angle to the base also serves as the median and angle bisector. If you see two sides that appear equal or two angles that look the same, it's likely isosceles.

What's the difference between equilateral and isosceles triangles?

Equilateral triangles have all three sides equal and all three angles equal to 60°. Isosceles triangles have only two equal sides and two equal angles. Every equilateral triangle is also isosceles, but not every isosceles triangle is equilateral.

Why do all triangle angles always add up to 180 degrees?

This is a fundamental property of Euclidean geometry. When you draw any triangle on a flat surface, the three interior angles will always sum to exactly 180°. This rule helps us solve for unknown angles and is essential for triangle classification and problem-solving.

How do you solve triangle problems step by step?

Follow these steps: 1) Identify what type of triangle you have, 2) List the given information (sides, angles), 3) Determine what you need to find, 4) Apply the appropriate formula or property (angle sum, Pythagorean theorem, etc.), 5) Solve algebraically, 6) Check your answer makes sense.

What are common mistakes students make with triangle problems?

Common errors include: forgetting that angles must sum to 180°, confusing triangle types, incorrectly applying the Pythagorean theorem to non-right triangles, mixing up which side is the hypotenuse, and not checking if their calculated angles or sides create a valid triangle.

Triangle Practice Problems: Types, Properties & Geometry

Understanding Triangle