Area and Perimeter of Composite Figures

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.

Imagine Kai and Maya are on a math adventure, exploring the mysteries of shapes and areas! They come across a magical rectangle and a mystical semi-circle. With a sparkle in their eyes, they calculate the area of the rectangle to be (a)   and then, with a wave of their math wands, find the area of the semi-circle to be (b)   . Combining their findings, they discover that the total area of their magical shapes is (c)   . Help Kai and Maya confirm their calculations.

• 100

• 39.25

• 139.25

• 78.5

• 314

• 178.5

Answer explanation

The correct answer is 100 because the area of the rectangle is 39.25 and the area of the semi-circle is 39.25, resulting in a total area of 100.

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.

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.

What is the perimeter of the following figure?

• 73.68 ft

• 54.85 ft

• 37.68 ft

• 97.68 ft

Find the perimeter of this figure

• 15.7in

• 55.7in

• 30.7in

• 40.7in

What is the area of the composite figure?

• 144 m²

• 111 m²

• 45 m²

• 70 m²

What is the area of the composite shape?

• 40ft²

• 9ft²

• 49ft²

• 61ft²

What is the area of the composite shape?

• 50cm²

• 25cm²

• 40cm²

• 35cm²