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Decomposing Bases for Area
Directions: A house-shaped prism is created by attaching a triangular prism on top of a ectangular prism. An image of the prism is shown. Answer the questions about the prism.
What is the area of the base?
how your work.

Draw the base of this prism and label the dimensions.
What is the volume of the prism? Show your work.

Decomposing Bases for Area $\newline$ Directions: A house-shaped prism is created by attaching a triangular prism on top of a ectangular prism. An image of the prism is shown. Answer the questions about the prism. $\newline$ What is the area of the base? $\newline$ how your work. $\newline$ $1$ . Draw the base of this prism and label the dimensions. $\newline$ $3$ . What is the volume of the prism? Show your work.

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Area of quadrilaterals and triangles: word problems

Full solution

Q. Decomposing Bases for Area

\newline

Directions: A house-shaped prism is created by attaching a triangular prism on top of a ectangular prism. An image of the prism is shown. Answer the questions about the prism.

\newline

What is the area of the base?

\newline

how your work.

\newline

1

. Draw the base of this prism and label the dimensions.

\newline

3

. What is the volume of the prism? Show your work.

Calculate Base Area: To find the area of the base, we need to add the area of the rectangle and the area of the triangle.
Rectangle and Triangle: Let's say the rectangle has dimensions length $l$ and width $w$ , and the triangle has a base $b$ (same as width $w$ of the rectangle) and height $h$ .
Rectangle Area: Area of the rectangle is $l \times w$ .
Triangle Area: Area of the triangle is $(b \times h) / 2$ .
Total Base Area: Now, we add the area of the rectangle and the area of the triangle to get the total area of the base.
Dimension Error: Total area of the base = $(l \times w) + \left(\frac{b \times h}{2}\right)$ .
Dimension Error: Total area of the base = $(l \times w) + \left(\frac{b \times h}{2}\right)$ . But we made a mistake, we don't have the actual dimensions. Without the dimensions, we can't calculate the area.

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\newline

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