The formulas used in the calculations are:
Determine Angle Measurements:
\[ 2a + b = 180 \]
Perimeter:
\[ \text{Perimeter} = 2A + B \]
Area:
\[ \text{Area} = \frac{1}{2} B \times H \]
An isosceles triangle is identified by two equal base angles and two opposing sides of equal length. Knowing one angle measurement allows you to determine the other angles using the formula \( 2a + b = 180 \). The perimeter is found using \( \text{Perimeter} = 2A + B \). The area is calculated using the formula \( \text{Area} = \frac{1}{2} B \times H \).
Determine Angle Measurements:
Calculate angle a:
\[ 2a + 90 = 180 \implies 2a = 90 \implies a = 45 \text{ degrees} \]
Calculate Perimeter:
\[ \text{Perimeter} = 2(6) + 4 = 16 \text{ units} \]
Calculate Area:
\[ \text{Area} = \frac{1}{2} \times 8 \times 26 = 104 \text{ cm}^2 \]