Understanding Area of Shapes Quiz

Anika is planning to build a rectangular garden in her backyard. What is the formula for the area of the garden?

Answer explanation

The area of a rectangle is calculated by multiplying its length (l) by its width (w). Therefore, the correct formula is l \times w, which represents the total space within the rectangle.

Tags

CCSS.3.MD.C.7B

CCSS.4.MD.A.3

Charlotte is planning to tile her kitchen floor, which is in the shape of a rectangle. The floor has a length of 8 cm and a width of 5 cm. What is the area of the floor that she needs to cover with tiles?

• 13 cm²

• 40 cm²

• 20 cm²

• 80 cm²

Answer explanation

The area of a rectangle is calculated by multiplying its length by its width. Here, area = 8 cm × 5 cm = 40 cm². Therefore, the correct answer is 40 cm².

Tags

CCSS.3.MD.C.7B

CCSS.4.MD.A.3

Charlotte is helping her friend paint a triangular garden. What is the formula for the area of the triangle?

Answer explanation

The area of a triangle is calculated using the formula \(\frac{1}{2} \times b \times h\), where \(b\) is the base and \(h\) is the height. This formula accounts for the triangular shape, making it the correct choice.

Tags

CCSS.6.G.A.1

Henry is building a triangular garden with a base of 10 cm and a height of 6 cm. What is the area of the garden?

• 30 cm²

• 60 cm²

• 20 cm²

• 40 cm²

Answer explanation

The area of a triangle is calculated using the formula: Area = 1/2 × base × height. Here, Area = 1/2 × 10 cm × 6 cm = 30 cm². Thus, the correct answer is 30 cm².

Tags

CCSS.6.G.A.1

Maya is designing a garden in the shape of a trapezoid. What is the formula for the area of a trapezoid?

Answer explanation

The area of a trapezoid is calculated using the formula \(\frac{1}{2} \times (b_1 + b_2) \times h\), where \(b_1\) and \(b_2\) are the lengths of the two parallel sides and \(h\) is the height. This formula averages the bases.

Tags

CCSS.6.G.A.1

Luna is designing a garden bed in the shape of a trapezoid. The longer base of the garden bed is 8 cm, the shorter base is 5 cm, and the height is 4 cm. What is the area of the garden bed?

• 26 cm²

• 52 cm²

• 20 cm²

• 40 cm²

Answer explanation

The area of a trapezoid is calculated using the formula: Area = 1/2 * (base1 + base2) * height. Here, Area = 1/2 * (8 + 5) * 4 = 1/2 * 13 * 4 = 26 cm². Thus, the correct answer is 26 cm².

Tags

CCSS.6.G.A.1

Aria is planning to build a rectangular garden. If the area of the garden is 56 cm² and its width is 7 cm, what is its length?

• 8 cm

• 7 cm

• 6 cm

• 9 cm

Answer explanation

To find the length of the rectangle, use the formula: Area = Length × Width. Given Area = 56 cm² and Width = 7 cm, we can rearrange the formula to Length = Area / Width. Thus, Length = 56 cm² / 7 cm = 8 cm.

Tags

CCSS.3.MD.C.7B

CCSS.4.MD.A.3

Ava is helping her friend paint a triangular garden sign. If the area of the sign is 24 cm² and its base is 8 cm, what is its height?

• 3 cm

• 6 cm

• 4 cm

• 5 cm

Answer explanation

To find the height of the triangle, use the formula: Area = 1/2 * base * height. Rearranging gives height = (2 * Area) / base. Substituting the values: height = (2 * 24) / 8 = 6 cm. Thus, the height is 6 cm.

Tags

CCSS.6.G.A.1

Harper is designing a garden bed in the shape of a trapezoid. The garden bed has an area of 35 cm², one base of 5 cm, and a height of 5 cm. What is the length of the other base?

• 9 cm

• 10 cm

• 11 cm

• 12 cm

Answer explanation

The area of a trapezoid is given by the formula A = 1/2 * (b1 + b2) * h. Plugging in the values: 35 = 1/2 * (5 + b2) * 5. Solving for b2 gives b2 = 10 cm.

Tags

CCSS.6.G.A.1

Kai is planning to build a rectangular garden. The length of the garden is 12 m and the width is 3 m. What is the area of the garden?

• 36 m²

• 15 m²

• 24 m²

• 45 m²

Answer explanation

The area of a rectangle is calculated by multiplying the length by the width. Here, 12 m (length) x 3 m (width) = 36 m². Therefore, the correct answer is 36 m².

Tags

CCSS.3.MD.C.7B

CCSS.4.MD.A.3