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Rectangle & Triangle
Area

Master the formulas for calculating the area of rectangles and triangles, and see how they connect.

SSAT Middle Level: Quantitative

What Is Area?

Area measures the amount of flat space inside a two-dimensional shape. Think of it as counting how many unit squares fit inside a figure.

1 7 columns 4 rows = 28 sq units

Key Vocabulary

Base
Any side of a shape that you choose as the "bottom" for measurement.
Height
The perpendicular distance from the base to the opposite side (or vertex).
Perpendicular
Meeting at a \(90°\) right angle, shown by a small square symbol.

Why Does Area Matter?

Area shows up everywhere in real life: painting a wall, tiling a floor, or measuring a garden plot. On the SSAT, you need to calculate area quickly and accurately.

Real World
Buying carpet, wrapping a gift, covering a book.
SSAT Questions
Often pair area with word problems or multi-step geometry.

Area of a Rectangle

base (b) height (h) A B C D

Area of a Triangle

base (b) height (h) A B C

The Connection Between Them

Rectangle → Triangle 1 Triangle 2 One diagonal splits into two equal triangles = half the rectangle

Rectangle vs. Triangle

Rectangle Triangle
Sides 4 sides, all right angles 3 sides
Formula \(b \times h\) \(\frac{1}{2} \times b \times h\)
Height Always a side May be inside or outside
Key Factor Full base × height Half of base × height

Step-by-Step Method

1
Identify the shape. Is it a rectangle or a triangle?
2
Find the base. Read the length labeled along the bottom (or any chosen side).
3
Find the height. It must be perpendicular (\(90°\)) to the base: not the slant side.
4
Apply the formula. Rectangle: \(b \times h\). Triangle: \(\frac{1}{2} \times b \times h\).
5
Include units. Always write your answer in square units (\(\text{cm}^2\), \(\text{in}^2\), etc.).

Example 1: Rectangle

12 cm 8 cm

Example 2: Triangle

18 in 10 in A B C

Example 3: Combined Shape

A shape is made of a rectangle topped by a triangle. The rectangle is 10 m wide and 6 m tall. The triangle on top has the same 10 m base and a 4 m height.

10 m 6 m 4 m

Height Can Be Outside

A B C h base (BC)

Common Mistakes

✕ Forgetting \(\frac{1}{2}\)
Using \(b \times h\) for a triangle gives double the correct area. Always multiply by \(\frac{1}{2}\).
✕ Using Slant Height
The height must be perpendicular to the base: the slant side of a triangle is not the height.
✕ Wrong Units
Area is in square units. Writing "cm" instead of "\(\text{cm}^2\)" costs points on the SSAT.

Quick Reference Summary

Property Rectangle Triangle
Formula \(A = b \times h\) \(A = \frac{1}{2} \times b \times h\)
Number of sides 4 3
Height location Always a side Inside, on a side, or outside
Relationship Triangle area = \(\frac{1}{2}\) of rectangle area (same base & height)
Units Always square units (\(\text{cm}^2, \text{m}^2, \text{in}^2\))

Question 1 of 5

A rectangle has a base of 15 cm and a height of 9 cm. What is its area?

Question 2 of 5

A triangle has a base of 14 in and a height of 6 in. What is its area?

Question 3 of 5

A rectangle has an area of \(72 \;\text{m}^2\) and a base of 12 m. What is its height?

Question 4 of 5

A triangle has sides of 13 cm, 10 cm, and 5 cm. Its height to the 10 cm base is 4 cm. What is the area?

Question 5 of 5

A rectangle is 20 ft wide and 8 ft tall. A triangle is cut from it using a diagonal. What is the area of one of those triangles?