Area Of Parallelograms, Triangles, & Trapezoids Quiz

Explanation
To find the area of a right triangle, you can use the formula:Area=12×base×heightIn the provided image, the base of the right triangle is 7 units and the height is 9 units. Plugging these values into the formula, we get:Area=12×7×9\text{Area} = \frac{1}{2} \times 7 \times 9Area=12×63\text{Area} = \frac{1}{2} \times 63Area=31.5\text{Area} = 31.5So, the area of the triangle is 31.5 square units.

Explanation
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.

Explanation
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.

Explanation
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.

Explanation
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.

Explanation
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.

Explanation
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.

Explanation
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}

Explanation
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}

 

Explanation
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}