Area

Triangles

100

A triangle has a base of 8 cm and a height of 5 cm. Find its area.

20 sq cm²

200

The base of a triangle is 12 m, and its area is 54 m². Find the height of the triangle.

9 meters

300

A triangle has sides of lengths 7 cm, 24 cm, and 25 cm. Find its area.

84 cm²

400

The vertices of a triangle are at points A(2,3), B(5,7), and C(8,3) on the coordinate plane. Find the area of the triangle.

12

500

A triangle has sides of length 13 cm, 14 cm, and 15 cm. Use Heron's formula to find its area.

The formula is: Area = √(s(s-a)(s-b)(s-c))

84 sq cm²

Squares

100

What is the formula for finding the area of a square?

• A) side × side
• B) side + side
• C) side ÷ side
• D) side - side

A) side x side

200

A square has a side length of 4 cm. What is its area?

Area = 4 cm × 4 cm = 16 cm²

300

The area of a square is 81 square meters. What is the length of one side?

Side = √81 = 9 meters

400

If the side of a square is doubled, by what factor does the area increase?

 The area increases by a factor of 4 (since area = side², doubling the side means area = (2 × side)² = 4 × original area)

500

A square and a rectangle have the same area. The rectangle’s length is twice its width, and the square’s side length is 12 cm. What are the dimensions of the rectangle?

• Area of square = 12 cm × 12 cm = 144 cm²
• Let width of rectangle = w cm, length = 2w cm
• Area of rectangle = w × 2w = 2w²
• Set equal: 2w² = 144 → w² = 72 → w = √72 ≈ 8.49 cm
• Length = 2 × 8.49 ≈ 16.98 cm
• Rectangle dimensions: approximately 8.49 cm by 16.98 cm

Rectangle

100

What is the formula to calculate the area of a rectangle?

Formula: Area = Length × Width

200

A rectangle has a length of 8 cm and a width of 3 cm. What is its area?

Area = 8 cm × 3 cm = 24 cm²

300

The area of a rectangle is 60 square meters, and its length is 12 meters. What is the width?

Given Area = 60 m², Length = 12 m
Width = Area ÷ Length = 60 ÷ 12 = 5 m

400

If the length of a rectangle is doubled and the width is halved, how does the area change?

L × W
New Area = (2 × L) × (W ÷ 2) = 2L × (W/2) = L × W
So, the area remains the same.

500

A rectangle's length is 5 cm more than twice its width. If the area is 150 square centimeters, find the dimensions of the rectangle.

 Let width = w cm
Length = 2w + 5 cm
Area = Length × Width = 150
So, (2w + 5) × w = 150
2w² + 5w - 150 = 0
Solve quadratic equation:
w = [-5 ± √(25 + 1200)] / 4 = [-5 ± √1225] / 4 = [-5 ± 35] / 4
Taking positive root: (−5 + 35)/4 = 30/4 = 7.5 cm
Length = 2(7.5) + 5 = 15 + 5 = 20 cm
Dimensions: Width = 7.5 cm, Length = 20 cm

Trapezoid

100

What is the formula to find the area of a trapezoid?

Area = a plus b divided by 2 times height

200

A trapezoid has bases of lengths 6 cm and 10 cm, and a height of 4 cm. What is its area?

A=a+b/2 h = 6 + 10/2 4 = 32