Area Of Parallelograms, Triangles, & Trapezoids Quiz

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.


Rectangle:


Width: 9 meters
Height: 15 meters


Area of Rectangle=Width×Height
Area of Rectangle=9×15=135 square meters



Right Triangle:


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


Area of Triangle=12×Base×Height


Area of Triangle=12×11×15=12×165=82.5 square meters\text{Area of Triangle} = \frac{1}{2} \times 11 \times 15 = \frac{1}{2} \times 165 = 82.5 \text{ square meters}


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


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



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

The given shape is a trapezoid. To find the area of a trapezoid, you can use the formula:Area=12×(Base1+Base2)×Height\text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}From the image:Base 1 (b1): 6 meters (the longer base)Base 2 (b2): 6 meters (the shorter base, since both bases are equal in this trapezoid)Height (h): 2.5 metersNow, we can plug these values into the formula:Area=12×(6+6)×2.5\text{Area} = \frac{1}{2} \times (6 + 6) \times 2.5Area=12×12×2.5\text{Area} = \frac{1}{2} \times 12 \times 2.5Area=6×2.5\text{Area} = 6 \times 2.5Area=15 square meters\text{Area} = 15 \text{ square meters}So, the area of the trapezoid is 15 square meters.

To find the area of the given right triangle, we use the formula for the area of a triangle:Area=12×base×height\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}In the image:Base: 5 metersHeight: 12 metersNow, plug these values into the formula:Area=12×5×12\text{Area} = \frac{1}{2} \times 5 \times 12Area=12×60\text{Area} = \frac{1}{2} \times 60Area=30 square meters\text{Area} = 30 \text{ square meters}So, the area of the triangle is 30 square meters.

To find the area of the given trapezoid, we use the formula for the area of a trapezoid:Area=12×(Base1+Base2)×Height\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 feetNow, we can plug these values into the formula:Area=12×(18+8)×5\text{Area} = \frac{1}{2} \times (18 + 8) \times 5Area=12×26×5\text{Area} = \frac{1}{2} \times 26 \times 5Area=13×5\text{Area} = 13 \times 5Area=65 square feet\text{Area} = 65 \text{ square feet}So, the area of the trapezoid is 65 square feet.

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

A=34s2A = \frac{\sqrt{3}}{4} s^2A

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

A=34×252

A=34×625A = \frac{\sqrt{3}}{4} \times 625

A=156.253A = 156.25 \sqrt{3}​

A≈270.63 square unitsA \approx 270.63 \text{ square units}

So, the correct answer is 270.63 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.

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

Area=12×base×height\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:

Area=12×10×2.5\text{Area} = \frac{1}{2} \times 10 \times 2.5

Area=12×25\text{Area} = \frac{1}{2} \times 25

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

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}

Given:


Base 1 (Base1\text{Base}_1​) = 10 units
Base 2 (Base2\text{Base}_2​) = 6 units
Height (Height\text{Height}) = 4 units


Area=12×(10+6)×4

Area=12×16×4\text{Area} = \frac{1}{2} \times 16 \times 4

Area=8×4\text{Area} = 8 \times 4

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

 

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}Given:Base 1 (Base1\text{Base}_1​) = 12 unitsBase 2 (Base2\text{Base}_2​) = 8 unitsHeight (Height\text{Height}) = 5 unitsArea=12×(12+8)×5\text{Area} = \frac{1}{2} \times (12 + 8) \times 5Area=12×20×5\text{Area} = \frac{1}{2} \times 20 \times 5Area=10×5\text{Area} = 10 \times 5Area=50 square units\text{Area} = 50 \text{ square units}