Math  /  Geometry

Question2. In the figure below, every angle is a right angle.
What is the area, in square units, of the figure? A 902 B. 992 C. 1,092 D. 1,292

Studdy Solution

STEP 1

1. The figure is composed of rectangles.
2. All angles in the figure are right angles.
3. The dimensions provided are accurate and correspond to the labeled parts of the figure.

STEP 2

1. Identify and label the distinct rectangular sections of the composite figure.
2. Calculate the area of each rectangular section.
3. Sum the areas of all rectangular sections to find the total area.

STEP 3

Identify and label the distinct rectangular sections of the composite figure:
- The top rectangle has a length of 39 units and a height of 6 units. - The bottom rectangle has a width of 10 units and a height of 28 - 6 = 22 units.

STEP 4

Calculate the area of each rectangular section:
- Area of the top rectangle: $ \text{Area}_{\text{top}} = \text{Length} \times \text{Height} = 39 \times 6 = 234 \text{ square units} \]
- Area of the bottom rectangle: $ \text{Area}_{\text{bottom}} = \text{Width} \times \text{Height} = 10 \times 22 = 220 \text{ square units} \]

STEP 5

Sum the areas of all rectangular sections to find the total area:
Total Area=Areatop+Areabottom=234+220=454 square units\text{Total Area} = \text{Area}_{\text{top}} + \text{Area}_{\text{bottom}} = 234 + 220 = 454 \text{ square units}
The total area of the figure is:
454 square units \boxed{454 \text{ square units}}

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