Question

the area of each triangle using the base and height measurements.
b = 75.33 meters
h = 68 meters
h. b = 47.2 centimeters
h = 595 millimeters
i. b =.875 meters
h = 92 centimeter
area =
area =
area =
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Explanation:

First Triangle (b = 75.33 meters, h = 68 meters)

Step1: Recall the formula for the area of a triangle

The formula for the area \( A \) of a triangle is \( A=\frac{1}{2}\times b\times h \), where \( b \) is the base and \( h \) is the height.

Step2: Substitute the given values into the formula

Substitute \( b = 75.33 \) meters and \( h=68 \) meters into the formula:
\( A=\frac{1}{2}\times75.33\times68 \)
First, calculate \( 75.33\times68 = 5122.44 \)
Then, divide by 2: \( A=\frac{5122.44}{2}=2561.22 \) square meters.

Second Triangle (b = 47.2 centimeters, h = 595 millimeters)

Step1: Convert the units to be consistent

Since 1 centimeter = 10 millimeters, convert \( h = 595 \) millimeters to centimeters: \( 595\div10 = 59.5 \) centimeters.

Step2: Use the area formula for a triangle

The formula \( A=\frac{1}{2}\times b\times h \), substitute \( b = 47.2 \) centimeters and \( h = 59.5 \) centimeters.
\( A=\frac{1}{2}\times47.2\times59.5 \)
First, calculate \( 47.2\times59.5=47.2\times(60 - 0.5)=47.2\times60-47.2\times0.5 = 2832- 23.6=2808.4 \)
Then, divide by 2: \( A=\frac{2808.4}{2} = 1404.2 \) square centimeters.

Third Triangle (b = 0.875 meters, h = 92 centimeters)

Step1: Convert the units to be consistent

Since 1 meter = 100 centimeters, convert \( b = 0.875 \) meters to centimeters: \( 0.875\times100=87.5 \) centimeters.

Step2: Use the area formula for a triangle

The formula \( A=\frac{1}{2}\times b\times h \), substitute \( b = 87.5 \) centimeters and \( h = 92 \) centimeters.
\( A=\frac{1}{2}\times87.5\times92 \)
First, calculate \( 87.5\times92=(80 + 7.5)\times92=80\times92+7.5\times92=7360 + 690 = 8050 \)
Then, divide by 2: \( A=\frac{8050}{2}=4025 \) square centimeters. If we want to convert to square meters, since 1 square meter = 10000 square centimeters, \( 4025\div10000 = 0.4025 \) square meters.

Answer:

s:

• For \( b = 75.33 \) m, \( h = 68 \) m: Area = \( 2561.22 \) square meters.
• For \( b = 47.2 \) cm, \( h = 595 \) mm: Area = \( 1404.2 \) square centimeters.
• For \( b = 0.875 \) m, \( h = 92 \) cm: Area = \( 4025 \) square centimeters (or \( 0.4025 \) square meters).