Talulah drew the net shown on a piece of cardboard. She plans to cut it out to make an odd-shaped gift box.
The pattern has three rectangles side by side. The shorter side of the rectangles is 3 c-m, the lengths of rectangles are 4 c-m, 3 c-m, and 5 c-m respectively. The middle rectangle has a right triangle above it and a right triangle below it. The measurements of the right triangle are 3 c-m, 4 c-m, and 5 c-m.
What is the surface area of the gift box?
A.
28 cm2
B.
42 cm2
C.
48 cm2
D.
56 cm2
D. 56 cm2
To find the surface area of the gift box, we need to calculate the areas of all the individual rectangles and triangles and then add them up.
Step 1: Calculate the area of the three rectangles.
Rectangle 1: Length = 4 cm, Width = 3 cm
Area = Length × Width = 4 cm × 3 cm = 12 cm²
Rectangle 2: Length = 3 cm, Width = 3 cm
Area = Length × Width = 3 cm × 3 cm = 9 cm²
Rectangle 3: Length = 5 cm, Width = 3 cm
Area = Length × Width = 5 cm × 3 cm = 15 cm²
Step 2: Calculate the area of the two right triangles.
Triangle 1: Base = 3 cm, Height = 4 cm
Area = (Base × Height) / 2 = (3 cm × 4 cm) / 2 = 6 cm²
Triangle 2: Base = 3 cm, Height = 4 cm
Area = (Base × Height) / 2 = (3 cm × 4 cm) / 2 = 6 cm²
Step 3: Add up the areas of all the shapes.
Total Surface Area = Area of Rectangle 1 + Area of Rectangle 2 + Area of Rectangle 3 + Area of Triangle 1 + Area of Triangle 2
Total Surface Area = 12 cm² + 9 cm² + 15 cm² + 6 cm² + 6 cm²
Total Surface Area = 48 cm²
Therefore, the surface area of the gift box is 48 cm².
The correct answer is C. 48 cm².
To find the surface area of the gift box, we need to calculate the areas of each of the rectangular faces and the two triangular faces.
First, let's find the areas of the rectangular faces. The rectangles have dimensions of 4 cm by 3 cm, 3 cm by 3 cm, and 5 cm by 3 cm.
Area of the first rectangle = 4 cm * 3 cm = 12 cm^2
Area of the second rectangle = 3 cm * 3 cm = 9 cm^2
Area of the third rectangle = 5 cm * 3 cm = 15 cm^2
Next, let's calculate the areas of the two triangular faces. The right triangles have side lengths of 3 cm, 4 cm, and 5 cm.
Area of the first triangle = (1/2) * base * height = (1/2) * 4 cm * 3 cm = 6 cm^2
Area of the second triangle = (1/2) * base * height = (1/2) * 4 cm * 3 cm = 6 cm^2
Now, let's add up the areas of all the faces to find the total surface area of the gift box.
Total surface area = Area of first rectangle + Area of second rectangle + Area of third rectangle + Area of first triangle + Area of second triangle
Total surface area = 12 cm^2 + 9 cm^2 + 15 cm^2 + 6 cm^2 + 6 cm^2
Total surface area = 48 cm^2
Therefore, the surface area of the gift box is 48 cm^2.
The correct answer is option C) 48 cm^2.