Help me slice and dice

What does it mean to decompose a figure?

• To color the figure

• To erase parts of the figure

• To draw the figure again

• To break it into smaller, familiar shapes

Which shapes are considered familiar figures?

• Stars and hearts

• Squares, rectangles, and trapezoids

• Clouds and trees

• Animals and cars

How can the total area of flooring needed be determined from a blueprint?

• By guessing the area

• By measuring the blueprint with a ruler

• By decomposing into rectangles or composing into a larger rectangle and subtracting unused areas

• By asking a friend

What is the importance of organizing your work when calculating areas?

• It is not important

• It helps in finding the correct answer more efficiently

• It takes more time

• It makes your work look neat

Which method is more efficient for calculating the area of composite figures?

• Using as many shapes as possible

• Breaking it down into the least amount of shapes necessary

• Calculating without breaking down the shapes

• Guessing the area based on experience

Elijah and Henry are on a treasure hunt and stumble upon a mysterious map. The map shows a treasure chest hidden behind a secret door. To open the door, they need to calculate the area of a magical seal. The seal is a composite figure made up of a rectangle with dimensions 5 cm by 8 cm and a triangle with base 6 cm and height 4 cm. Can you help them find the area of the seal to grab the treasure?

• 38 cm^2

• 50 cm^2

• 30 cm^2

• 44 cm^2

Answer explanation

To find the area of the composite figure, calculate the area of the rectangle (5*8=40 cm^2) and the area of the triangle (0.5*6*4=12 cm^2), then add them together (40+12=44 cm^2). Therefore, the correct answer is 44 cm^2.

Maya and Scarlett are on a treasure hunt in a magical land. They stumble upon a mysterious map that leads to a treasure chest. The map shows a path marked by a square garden with side length 10 cm and a magical gate shaped like a semicircle with a diameter of 12 cm. To unlock the next clue, they need to calculate the perimeter of this enchanted path. Can you help them find the perimeter of this composite figure?

• Perimeter is 60 cm

• Perimeter is 55.5 cm

• Perimeter is exactly 50 cm

• Perimeter is approximately 58.85 cm

Answer explanation

The perimeter of the composite figure is the sum of the sides of the square (4*10) and half the circumference of the semicircle (0.5*π*12). Calculating this gives approximately 58.85 cm.

Imagine Benjamin and Emma are on a magical math adventure and stumble upon a mysterious room. In the center, there's a magical artifact shaped like a cylinder with a radius of 5 cm and height of 10 cm, standing atop a cone with a radius of 3 cm and height of 6 cm. They need to figure out the volume of this composite figure to unlock the next door. Can you help them calculate it?

• 150π cm^3

• 320π cm^3

• 200π cm^3

• 268π cm^3

Answer explanation

The volume of the composite figure is the sum of the volumes of the cylinder and cone. Volume = πr^2h for cylinder and (1/3)πr^2h for cone. Calculating gives 268π cm^3.

Imagine Abigail and Emma are on a treasure hunt in a magical land. They come across a mysterious map that shows a treasure hidden under a shape that is a combination of a parallelogram and a trapezoid. The parallelogram part of the map has a base of 12 cm and a height of 8 cm, while the trapezoid part has bases of 6 cm and 10 cm with a height of 5 cm. Help Abigail and Emma calculate the area of this composite figure to find the treasure!

• 96 sq cm

• 72 sq cm

• 136 sq cm

• 50 sq cm

Answer explanation

To find the area of the composite figure, calculate the area of the parallelogram (12*8) and the trapezoid ((6+10)*5/2), then add them together (96 + 40 = 136 sq cm).

Imagine Michael, Daniel, and Anika are on an adventure in a magical land. They come across a mysterious gate guarded by a puzzle. The gate is made up of an equilateral triangle with a side length of 9 cm and a regular hexagon with a side length of 4 cm. To unlock the gate and continue their adventure, they need to find the perimeter of this composite figure. Can you help them solve this puzzle?

• 36 cm

• 45 cm

• 57 cm

• 51 cm

Answer explanation

To find the perimeter, add the side lengths of the equilateral triangle (3 sides of 9 cm each) and the regular hexagon (6 sides of 4 cm each), giving a total of 27 cm + 24 cm = 51 cm.