Area and Decomposing Shapes

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.

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 Charlotte and Emma are on an adventure in a mystical land filled with ancient structures. They stumble upon a magical chest that's guarded by a puzzle. The chest sits atop a rectangular prism pedestal with dimensions 6 cm by 4 cm by 5 cm. Right next to it, there's a pyramid with a square base of side length 3 cm and a height of 7 cm. To unlock the chest, they need to calculate the total surface area of these two structures combined. Can you help them solve this puzzle?

• 171 cm^2

• 120 cm^2

• 145 cm^2

• 160 cm^2

Answer explanation

To find the total surface area, calculate the sum of the lateral surface area of the rectangular prism (2(6*5 + 4*5)) and the lateral surface area of the pyramid (4*(1/2*3*7)). Add these together to get 120 + 51 = 171 cm^2.

Imagine Benjamin and Olivia are on a treasure hunt in a magical land. They stumble upon a secret garden where they find a circle-shaped pond with a radius of 10 cm and a square-shaped flower bed with a side length of 12 cm. Aria, the guardian of the garden, challenges them to calculate the area of this composite figure to pass through. Can you help them solve this puzzle?

• The area of the composite figure is approximately 471.24 cm^2.

• The area of the composite figure is approximately 300.50 cm^2.

• The area of the composite figure is exactly 500 cm^2.

• The area of the composite figure is 1000 cm^2.

Answer explanation

The correct answer is the area of the composite figure is approximately 471.24 cm^2 because it involves calculating the area of a circle and a square separately, then adding them together.

Imagine Aria, Rohan, and Anika are on a treasure hunt. They stumble upon an ancient map with a figure drawn on it. The map holds the key to the next clue, but to proceed, they need to calculate the area of the figure. Can you help them figure it out?

Answer explanation

The correct answer is 275 cm^2 because the figure is a rectangle with dimensions 25 cm by 11 cm, so the area is 25 * 11 = 275 cm^2.

Charlotte, Aria, and Nora are playing in the park when they come across a curious puzzle on the ground. It's a beautifully designed garden with a mix of shaded and unshaded regions. They wonder, 'What is the area of the unshaded region?' (a)  

Answer explanation

The area of the unshaded region is equal to the area of the larger square minus the area of the smaller square, which is 16 ft^2.

Find the area.

HINT: You will need to imagine two separate rectangles.

Area of rectangle = b (h)

Mathematical Equivalence

ON

Hey there! Mason, Benjamin, and Evelyn are on a treasure hunt in a magical land. They stumble upon a mysterious map that shows a shaded region. Can you help them figure out the area of this shaded region to find the treasure?

• 4

• 7.14

• 16.56

• 0.86

Answer explanation

The area of the shaded region is calculated by subtracting the area of the smaller circle from the area of the larger circle. Therefore, the correct answer is 0.86.

Match the following

• Area of trapezoid

• 60 square mm

• Area of parallelogram

• a figure composed of two or more two-dimensional figures

• Area of composite figure

• the number of square units a figure covers

• area

• 44 square mm

• composite figure

• 104 square mm

Imagine Zoe and Harper are on a treasure hunt in Jackson's magical garden. They stumble upon a mystical circle with a RADIUS of 7 inches. (a)   What's the area of this magical circle?

• 153.93 in2

• 115.43 in2

• 307.89 in2

• 203.86 in2

Answer explanation

The area of a circle is calculated using the formula A = πr^2. Substituting r=7 into the formula gives A = π(7)^2 = 153.93 in2. Therefore, the correct answer is 153.93 in2.