Determine the area of triangle ABC correct to one decimal place

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The problem asks to determine the area of triangle ABC, correct to one decimal place. The image shows a quadrilateral labeled ABCD with side lengths and a right angle.

Interpret the given diagram.
The figure appears to be a rectangle with vertices B, A, C, D.
The top side AB is labeled 120 cm.
The left vertical side is labeled 60 cm. Although the label "60" is placed on the segment BD, the visual representation and the right angle symbol at D strongly suggest that the figure is a rectangle with sides 120 cm and 60 cm. In a rectangle, the side AD (or BC) would be the width. We will assume the width is 60 cm.
The right angle symbol at D indicates that $\angle ADC = 90^\circ$ , which is consistent with a rectangle.
Identify the dimensions of triangle ABC.
In a rectangle, all angles are $90^\circ$ . Therefore, $\angle B$ in triangle ABC is $90^\circ$ .
Triangle ABC is a right-angled triangle with base $AB = 120$ cm and height $BC = 60$ cm (since opposite sides of a rectangle are equal, $BC = AD = 60$ cm).
Calculate the area of triangle ABC.
The area of a right-angled triangle is given by the formula:
$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$
Substitute the values for triangle ABC:
$\text{Area}_{\triangle ABC} = \frac{1}{2} \times AB \times BC$ $\text{Area}_{\triangle ABC} = \frac{1}{2} \times 120 \text{ cm} \times 60 \text{ cm}$ $\text{Area}_{\triangle ABC} = 60 \times 60 \text{ cm}^2$ $\text{Area}_{\triangle ABC} = 3600 \text{ cm}^2$
Round the answer to one decimal place.
$\text{Area}_{\triangle ABC} = \boxed{3600.0 \text{ cm}^2}$

Determine the area of triangle ABC correct to one decimal place

Answer

Step-by-step solution

Interpret the given diagram.

Identify the dimensions of triangle ABC.

Calculate the area of triangle ABC.

Round the answer to one decimal place.

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