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Question

An illustration shows rectangle extending to a triangle on the right. The top of the rectangle extends as the hypotenuse toward the bottom. The dimensions of the figure are as follows: the top is 8 centimeters, the left is 4 centimeters, and the bottom is 10 centimeters, including the side of the extended triangle.
What is the area of the figure in square centimeters?(1 point)

Answer 1

To find the area of the figure, we can break it down into two parts: the rectangle and the triangle.

1. Area of the Rectangle:

   • The width (or base) of the rectangle is 8 centimeters.
   • The height of the rectangle is 4 centimeters.
   • Area of the rectangle = width × height = 8 cm × 4 cm = 32 cm².

2. Area of the Triangle:

   • The base of the triangle is the bottom of the rectangle, which is part of the complete base of the figure, given as 10 centimeters.
   • The height of the triangle can be inferred from the right-angle triangle created by the extension. Since the triangle shares its height with the rectangle, we take the height from the rectangle = 4 centimeters.
   • Area of the triangle = (1/2) × base × height = (1/2) × 10 cm × 4 cm = 20 cm².

3. Total Area:

   • Now, we combine the areas of both shapes:
   • Total Area = Area of Rectangle + Area of Triangle = 32 cm² + 20 cm² = 52 cm².

Thus, the total area of the figure is 52 square centimeters.