Area Of Parallelograms, Triangles, & Trapezoids Quiz

To determine the area of a triangle, you can use the formula:

$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$

Given:

• Base = 10 units


• Height = 2.5 units

Plugging these values into the formula:

$\text{Area} = \frac{1}{2} \times 10 \times 2.5$

$\text{Area} = \frac{1}{2} \times 25$

$\text{Area} = 12.5 \text{ square units}$

Using the given base (7 units) and height (5 units):

Area=base×height

Area=7×5

Area=35 square units

So, the correct answer is 35 square units.

The formula for the area of a trapezoid is:

$\text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}$

Given:

• Base 1 ($\text{Base}_1$) = 10 units


• Base 2 ($\text{Base}_2$) = 6 units


• Height ($\text{Height}$) = 4 units

$\text{Area}=\frac{1}{2}\times (10+6)\times$4

$\text{Area} = \frac{1}{2} \times 16 \times 4$

$\text{Area} = 8 \times 4$

$\text{Area} = 32 \text{ square units}$

To find the area of the given right triangle, we use the formula for the area of a triangle:

$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$

In the image:

• Base: 5 meters
• Height: 12 meters

Now, plug these values into the formula:

$\text{Area} = \frac{1}{2} \times 5 \times 12$

$\text{Area} = \frac{1}{2} \times 60$

$\text{Area} = 30 \text{ square meters}$

So, the area of the triangle is 30 square meters.

The formula for the area of a trapezoid is:

$\text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}$

Given:

• Base 1 ($\text{Base}_1$) = 12 units
• Base 2 ($\text{Base}_2$) = 8 units
• Height ($\text{Height}$) = 5 units

$\text{Area} = \frac{1}{2} \times (12 + 8) \times 5$

$\text{Area} = \frac{1}{2} \times 20 \times 5$

$\text{Area} = 10 \times 5$

$\text{Area} = 50 \text{ square units}$

To find the area of the given shape, we need to break it down into simpler parts. The shape can be divided into a rectangle and a right triangle.

1. 
   

   Rectangle:

   
   
   
   
   
   • Width: 9 meters
   
   
   • Height: 15 meters
   
   
   
   
   

   $\text{Area of Rectangle}=\text{Width}\times \text{Height}$$$
   
   

   
   




3. 
   

   Right Triangle:

   
   
   
   
   
   • Base: 20 meters (total base) - 9 meters (width of rectangle) = 11 meters
   
   
   • Height: 15 meters
   
   
   
   
   

   $\text{Area of Triangle}=\frac{1}{2}\times \text{Base}\times \text{Height}$$$

   
   


4. 
   

   $\text{Area of Triangle} = \frac{1}{2} \times 11 \times 15 = \frac{1}{2} \times 165 = 82.5 \text{ square meters}$

   
   


5. 
   

   Total Area: $\text{Total Area} = \text{Area of Rectangle} + \text{Area of Triangle}$

   
   


6. 
   

   $\text{Total Area} = 135 + 82.5 = 217.5 \text{ square meters}$

   
   

So, the area of the given shape is 217.5 square meters.

To find the area of the given trapezoid, we use the formula for the area of a trapezoid:

$\text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}$

From the image:

• Base 1 (b1): 18 feet (the longer base)
• Base 2 (b2): 8 feet (the shorter base)
• Height (h): 5 feet

Now, we can plug these values into the formula:

$\text{Area} = \frac{1}{2} \times (18 + 8) \times 5$

$\text{Area} = \frac{1}{2} \times 26 \times 5$

$\text{Area} = 13 \times 5$

$\text{Area} = 65 \text{ square feet}$

So, the area of the trapezoid is 65 square feet.

The area $A$ of an equilateral triangle can be calculated using the formula:

$A = \frac{\sqrt{3}}{4} s^2$

Where $s$ is the length of a side. Given $s = 25$

$A=\frac{\sqrt{3}}{4}\times 25^2$

$A = \frac{\sqrt{3}}{4} \times 625$

$A = 156.25 \sqrt{3}$

$A \approx 270.63 \text{ square units}$

So, the correct answer is 270.63 square units.