Question

consider the isosceles triangle, with the following dimensions: ab = ad = 5 cm. bc = cd = 3 cm. ac = 4 cm. what is the area of this isosceles triangle?

Explanation:

Step1: Determine the base length

First, find the length of the base \( BD \). Since \( BC = CD = 3 \, \text{cm} \), we add them: \( BD = BC + CD = 3 + 3 = 6 \, \text{cm} \).

Step2: Identify height and apply area formula

The height of the isosceles triangle (from \( A \) to \( BD \)) is \( AC = 4 \, \text{cm} \). The formula for the area of a triangle is \( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \). Substitute base \( BD = 6 \, \text{cm} \) and height \( AC = 4 \, \text{cm} \): \( \text{Area} = \frac{1}{2} \times 6 \times 4 \).

Step3: Calculate the area

Simplify the expression: \( \frac{1}{2} \times 6 \times 4 = 3 \times 4 = 12 \, \text{cm}^2 \).

Answer:

The area of the isosceles triangle is \( 12 \, \text{cm}^2 \).