To find the area of the shape, we need to calculate the areas of each individual polygon and then add them up.
Rectangle (Center):
Area = length x width = 6 x 3 = 18 in²
Squares (Top and Bottom):
Area of each square = side x side = 3 x 3 = 9 in²
Total area of both squares = 2 x 9 = 18 in²
Trapezoids:
Top trapezoid area = 1/2 x (base1 + base2) x height
Top trapezoid area = 1/2 x (6 + 3) x 1 = 4.5 in²
Bottom trapezoid area = 1/2 x (base1 + base2) x height
Bottom trapezoid area = 1/2 x (3 + 6) x 1 = 4.5 in²
Left trapezoid area = 1/2 x (base1 + base2) x height
Left trapezoid area = 1/2 x (3 + 1.2) x 3 = 5.1 in²
Total area = rectangle area + squares area + top trapezoid area + bottom trapezoid area + left trapezoid area
Total area = 18 + 18 + 4.5 + 4.5 + 5.1 = 50.1 in²
Therefore, the area of the shape is 50.1 square inches.
Use the image to answer the question.
An illustration shows an unfolded box net. It is comprised of a rectangle at the center, two squares extending into three trapezoids on the top and bottom, and a trapezoid on the left of the rectangle. The top side of the rectangle is labeled in three distinct sections: starting at the left, a solid line of 3 is drawn, followed by a dashed line of 3, and then a solid line of 6. The bottom of the rectangle is labeled in three distinct sections: a solid line of 6, a dashed line of 3, and a solid line of 3. The left width of the rectangle is drawn as a dashed line, labeled as 3, which becomes the base of a shaded trapezoid. The dashed lines on the top and bottom of the rectangle are extended into squares of side 3, sides drawn in dashed lines. The three outer sides of each square become the longer bases of shaded trapezoids. The top shorter side of the trapezoid is labeled as 1.2 and the perpendicular height is 1.
Decompose the box net into simple polygons to find how much cardboard in square inches is needed to make the cube. Assume that all angles that look like right angles are right angles. All polygons that look congruent are congruent. What is the area of the shape in square inches?
1 answer
1 answer