Question

the diagram shows triangle abc. use the drop-down menus to make each statement true. the base of triangle abc is dropdown units. the height of triangle abc is dropdown units. the area of triangle abc is dropdown square units. calculator button diagram: triangle abc with points b, c, and a right angle vertex. lengths: bc=4.2, c to right angle=3.5, height from a to base=6.6, ab=10.1, ac=7.5. not drawn to scale

Explanation:

Step1: Identify the base

The base of triangle \( ABC \) is the length of \( BC \), which is given as \( 4.2 \) units.

Step2: Identify the height

The height corresponding to base \( BC \) is the vertical segment from \( A \) to the base (or its extension), which is \( 6.6 \) units.

Step3: Calculate the area

The formula for the area of a triangle is \( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \). Substituting the values, we get \( \text{Area} = \frac{1}{2} \times 4.2 \times 6.6 \). First, calculate \( 4.2 \times 6.6 = 27.72 \), then divide by 2: \( \frac{27.72}{2} = 13.86 \).

Answer:

The base of triangle \( ABC \) is \( 4.2 \) units.
The height of triangle \( ABC \) is \( 6.6 \) units.
The area of triangle \( ABC \) is \( 13.86 \) square units.