Area of Rectangles and Triangles

Show your work for each problem.

1.
A rectangle has a length of 6 cm and a width of 4 cm. What is its area?
1. a)12 cm²
2. b)20 cm²
3. c)24 cm²
4. d)10 cm²
Answer: 24 cm²
Area = cm². We multiply length by width to find the area of a rectangle.
2.
A triangle has a base of 10 cm and a height of 6 cm. What is its area in cm²?
Answer: 30
Area = cm². Remember to divide by 2 for triangles!
3.
Which formula is used to calculate the area of a triangle?
1. a)2 × base × height
2. b)base + height
3. c)base × height
4. d)½ × base × height
Answer: ½ × base × height
The formula for a triangle's area is . We multiply base by height, then divide by 2.
4.
A rectangular poster is 50 cm long and 30 cm wide. Calculate its area.
Answer: 1500
1. What is the length of the poster? 50
2. What is the width of the poster? 30
3. What is 50 × 30? 1500
5.
A square has sides of 7 m. What is its area in m²?
Answer: 49
Area = side × side = m². A square is a rectangle with all sides equal.
6.
A triangular garden has a base of 12 m and a height of 8 m. Calculate its area step by step.
Answer: 48
1. What is base × height? 96
2. What is 96 ÷ 2? 48
3. What are the correct units for area? m²
7.
A rectangle has an area of 72 cm² and a width of 8 cm. What is its length?
1. a)10 cm
2. b)8 cm
3. c)9 cm
4. d)7 cm
Answer: 9 cm
Length = Area ÷ width = cm. We can find a missing dimension by dividing the area by the known dimension.
8.
A rectangular floor is 9 m by 6 m. How many 1 m² tiles are needed to cover it?
Answer: 54
Area = m². Since each tile covers 1 m², we need 54 tiles.
9.
A right triangle has legs of 5 cm and 12 cm. Find its area.
Answer: 30
1. In a right triangle, which sides can be used as base and height? legs
2. What is 5 × 12? 60
3. What is 60 ÷ 2? 30
10.
A triangle has an area of 24 cm² and a base of 8 cm. What is its height?
1. a)3 cm
2. b)6 cm
3. c)4 cm
4. d)8 cm
Answer: 6 cm
Height = cm
11.
A rectangular room is 5 m by 4 m. Paint costs 15 euros per can and covers 10 m². How much does it cost to paint the floor?
Answer: 30
1. What is the floor area? (5 × 4) 20
2. How many cans of paint are needed? (20 ÷ 10) 2
3. What is the total cost? (2 × 15) 30
12.
A house wall consists of a rectangle (8 m × 3 m) with a triangular roof section on top (base 8 m, height 2 m). What is the total area in m²?
Answer: 32
Rectangle: m². Triangle: m². Total: m².
13.
An L-shaped room consists of two rectangles: one is 6 m × 4 m, the other is 3 m × 2 m. Find the total floor area.
Answer: 30
1. What is the area of the first rectangle? (6 × 4) 24
2. What is the area of the second rectangle? (3 × 2) 6
3. What is the total area? (24 + 6) 30
14.
If you double both the length and width of a rectangle, what happens to its area?
1. a)It doubles
2. b)It quadruples
3. c)It stays the same
4. d)It triples
Answer: It quadruples
If you double both dimensions, the new area is . The area becomes 4 times larger (quadruples)!
15.
A rectangular field is 120 m by 80 m. A farmer wants to plant grass at a cost of 2 euros per m². What is the total cost in euros?
Answer: 19200
Area = m². Cost = euros.