Right-Angled Trapezoid Area Practice Problems & Solutions

Master calculating the area of right trapezoids with step-by-step practice problems. Learn formulas, identify properties, and solve real-world geometry exercises.

📚Master Right-Angled Trapezoid Area Calculations
  • Apply the area formula: (base1 + base2) × height ÷ 2
  • Identify the height as the perpendicular side connecting right angles
  • Solve problems with given bases and height measurements
  • Calculate missing dimensions when area is provided
  • Recognize right-angled trapezoid properties and angle relationships
  • Work through multi-step word problems involving trapezoid areas

Understanding Area of a Trapezoid

Complete explanation with examples

Area of a right trapezoid

In order to calculate the area of a right-angled trapezoid, we will use the following formula:

Diagram of a right-angled trapezoid with the formula for calculating its area:  ( Base 1 + Base 2 ) × height (Base 1+Base 2)×height. The illustration highlights the two parallel bases, the height, and the application of the formula to find the area. Featured in a tutorial on calculating the area of trapezoids.


The formula for calculating the area of a right-angled trapezoid is the same as every trapezoid's area - the sum of the bases times the height divided by 2.

The leg connecting the 2 right angles is also the height of the trapezoid!

Detailed explanation

Practice Area of a Trapezoid

Test your knowledge with 21 quizzes

What is the area of the trapezoid ABCD?

999121212555AAABBBCCCDDDEEE

Examples with solutions for Area of a Trapezoid

Step-by-step solutions included
Exercise #1

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 #2

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:

(Base+Base)h2=Area \frac{(Base+Base)\cdot h}{2}=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 #3

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
Exercise #4

The trapezoid ABCD is shown below.

AB = 5 cm

DC = 9 cm

Height (h) = 7 cm

Calculate the area of the trapezoid.

555999h=7h=7h=7AAABBBCCCDDD

Step-by-Step Solution

The formula for the area of a trapezoid is:

Area=12×(Base1+Base2)×Height \text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}

We are given the following dimensions:

  • Base AB=5AB = 5 cm
  • Base DC=9DC = 9 cm
  • Height h=7h = 7 cm

Substituting these values into the formula, we have:

Area=12×(5+9)×7 \text{Area} = \frac{1}{2} \times (5 + 9) \times 7

First, add the lengths of the bases:

5+9=14 5 + 9 = 14

Now substitute back into the formula:

Area=12×14×7 \text{Area} = \frac{1}{2} \times 14 \times 7

Calculate the multiplication:

12×14=7 \frac{1}{2} \times 14 = 7

Then multiply by the height:

7×7=49 7 \times 7 = 49

Thus, the area of the trapezoid is 49 cm2^2.

Answer:

49 cm

Video Solution
Exercise #5

Given the following trapezoid:

AAABBBCCCDDD7115

Calculate the area of the trapezoid ABCD.

Step-by-Step Solution

To calculate the area of the trapezoid ABCD, we will follow these steps:

Given:

  • Base AB=7 AB = 7
  • Base CD=11 CD = 11
  • Height =5 = 5

Apply the trapezoid area formula:

The formula for the area of a trapezoid is:

A=12×(Base1+Base2)×Height A = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}

Substitute the values into the formula:

A=12×(7+11)×5 A = \frac{1}{2} \times (7 + 11) \times 5

Simplify the expression:

A=12×18×5 A = \frac{1}{2} \times 18 \times 5

Calculate:

A=12×90 A = \frac{1}{2} \times 90

Finally, compute the area:

A=45 A = 45

Thus, the area of trapezoid ABCD is 45 45 .

Answer:

45

Video Solution

Frequently Asked Questions

What is the formula for finding the area of a right-angled trapezoid?

+
The area of a right-angled trapezoid is (base1 + base2) × height ÷ 2. This is the same formula used for all trapezoids, where you add the parallel bases, multiply by the height, and divide by 2.

How do you identify the height in a right-angled trapezoid?

+
In a right-angled trapezoid, the height is the perpendicular side that connects the two right angles. This side is perpendicular to both parallel bases and represents the shortest distance between them.

What are the key properties of a right-angled trapezoid?

+
A right-angled trapezoid has these properties: 1) Two angles equal to 90 degrees each, 2) The side connecting the right angles is the height, 3) All angles sum to 360 degrees, 4) The two non-right angles sum to 180 degrees.

How do you solve trapezoid area problems when the area is given?

+
When the area is given, substitute known values into the formula and solve for the unknown. For example, if area = 25 and sum of bases = 10, then 25 = (10 × height) ÷ 2, so height = 5.

What's the difference between a right trapezoid and regular trapezoid area calculation?

+
The area formula is identical for both types: (base1 + base2) × height ÷ 2. The difference is that in right trapezoids, the height is easier to identify as it's the side connecting the two right angles.

Can you calculate trapezoid area if you only know the angles and one side?

+
No, you need at least the lengths of both parallel bases and the height to calculate the area. Knowing only angles and one side length is insufficient for area calculation using the standard formula.

What units should I use for trapezoid area answers?

+
Area is always expressed in square units (units²). If the measurements are in centimeters, the area is in cm². If in meters, then m². Always match your area units to the square of your linear measurement units.

How do right-angled trapezoids appear in real-world applications?

+
Right-angled trapezoids appear in architecture (roof designs, ramps), engineering (bridge supports), and landscaping (garden plots). Understanding their area calculation helps in material estimation and space planning.

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