Areas of rectangles, triangles and parallelograms

A rectangular noticeboard is to be covered with paper, with no overlap or waste. Which quantity measures how much of its front surface must be covered?

A square unit has two length directions

Area measures the size of a flat region. Imagine covering it without gaps or overlaps using equal unit squares

One square centimetre is the area of a square one centimetre long and one centimetre wide

One square metre is the area of a one-metre by one-metre square

The raised two describes square units; it does not tell you to square a finished area answer

Perimeter is the distance around the boundary and uses length units. Area is the region inside and uses square units

Count each row, then count the rows

This rectangle has four one-centimetre squares in each row and three rows

In general, length l gives the number of unit widths across each row, and width w gives the number of rows

The same formula works when a length is not a whole number: subdividing the unit squares accounts for the fractional rows or columns

A square is a rectangle with equal length and width. If each side is s, the formula becomes

Calculate the surface of a rectangular panel

A rectangular panel has length l of 8 cm and perpendicular width w of 5 cm

The base and height are the rectangle length and width

Calculate the area in cm². Give an exact whole number or decimal

Area measures the enclosed region in square units, not the boundary length

Use the rectangle length and its perpendicular width

Length multiplied by width counts the square units across all rows

Multiply perpendicular rectangle dimensions

Use the same side length in both directions

A rectangular panel has length l of 6 m and perpendicular width w of 6 m

The base and height are the rectangle length and width

Calculate the area in m². Give an exact whole number or decimal

Area measures the enclosed region in square units, not the boundary length

Use the rectangle length and its perpendicular width

Length multiplied by width counts the square units across all rows

Keep a square area distinct from its boundary length

A rectangle is 8 cm long and 3 cm wide. Which calculation finds its area?

Cut perpendicular to the base, not along a sloping side

ABCD is a parallelogram. Choose AB as the base b

DH is perpendicular to AB, so its length is the height h between the parallel base lines

Cut off triangle ADH along DH. Keep both pieces without stretching them

The sloping side AD is not the perpendicular distance between the base lines. It is not h

Move the cut triangle to make a rectangle

Translate the cut triangle ADH to the right so that A moves to B, D moves to C and H moves to E

The two pieces now make rectangle HECD with no overlap or gap

The rectangle has the same height h and the same base length b as the original parallelogram

Moving a piece does not change its area, so

The area uses the perpendicular height, not the sloping side length. The result also applies when the height meets an extension of the base

Use the marked perpendicular height

A parallelogram-shaped panel has base b of 9 cm and perpendicular height h of 4 cm

The marked height meets the chosen base at a right angle

Calculate the area in cm². Give an exact whole number or decimal

Area measures the enclosed region in square units, not the boundary length

Use the base and perpendicular height, not a sloping side

Changing a sloping side does not change this area if the base and perpendicular height stay fixed

Calculate area without a sloping-side length

A perpendicular height can meet the extended base

A parallelogram-shaped panel has base b of 8 cm and perpendicular height h of 6 cm

The perpendicular height meets the extended base outside the panel

Calculate the area in cm². Give an exact whole number or decimal

Area measures the enclosed region in square units, not the boundary length

Use the base and perpendicular height, not a sloping side

Changing a sloping side does not change this area if the base and perpendicular height stay fixed

Keep the original base length when extending its line

A parallelogram has base 10 cm, perpendicular height 4 cm and sloping side 5 cm. Which length must be multiplied by the base to find area?

Two identical triangles make a parallelogram

Diagonal BD divides parallelogram ABCD into two triangles, ABD and BCD

A half-turn about the midpoint of BD takes one triangle onto the other, so they have equal area

Triangle ABD and the parallelogram share base AB and its perpendicular height

Multiply the chosen base by its perpendicular height, then divide by two

The perpendicular height may be a boundary side in a right triangle, an inside segment, or an outside segment meeting the extended base

Extending the base line locates a height; it does not increase the length b of the original triangle base

Use perpendicular sides of a right triangle

A triangular panel has base b of 8 cm and perpendicular height h of 5 cm

The marked height meets the chosen base at a right angle

Calculate the area in cm². Give an exact whole number or decimal

Area measures the enclosed region in square units, not the boundary length

A triangle has half the area of a parallelogram with the same base and perpendicular height

Halving the base-height product accounts for the triangular region

Halve the full base-height rectangle product

Use an interior height rather than either sloping side

A triangular panel has base b of 10 cm and perpendicular height h of 6 cm

The marked height meets the chosen base at a right angle

Calculate the area in cm². Give an exact whole number or decimal

Area measures the enclosed region in square units, not the boundary length

A triangle has half the area of a parallelogram with the same base and perpendicular height

Halving the base-height product accounts for the triangular region

A whole-number product can have a half-unit area

Follow the outside perpendicular to the extended base

A triangular panel has base b of 7 m and perpendicular height h of 4 m

The perpendicular height meets the extended base outside the panel

Calculate the area in m². Give an exact whole number or decimal

Area measures the enclosed region in square units, not the boundary length

A triangle has half the area of a parallelogram with the same base and perpendicular height

Halving the base-height product accounts for the triangular region

Use the same formula for an obtuse triangle

First keep h fixed and move the top side sideways. Then keep the shift fixed and change h. Compare the full parallelogram area with the shaded triangular half. The base stays six units throughout

Which statement describes every allowed setting?

Keep the exact decimal product

Decimal dimensions use the same formulas as whole-number dimensions

Multiply the stated numbers exactly. For a triangle, halve that product

A result such as twenty-two and a half square centimetres is a valid area

These questions ask for an exact whole number or decimal, so do not round an intermediate product or the final answer

Check the size: a triangle must have half the base-height product, while a parallelogram uses the whole product

Multiply two decimal rectangle lengths

A rectangular panel has length l of 6.5 m and perpendicular width w of 4.2 m

The base and height are the rectangle length and width

Calculate the area in m². Give an exact whole number or decimal

Area measures the enclosed region in square units, not the boundary length

Use the rectangle length and its perpendicular width

Length multiplied by width counts the square units across all rows

Calculate an exact decimal area

Halve the exact decimal product

A triangular panel has base b of 8.5 cm and perpendicular height h of 3.2 cm

The marked height meets the chosen base at a right angle

Calculate the area in cm². Give an exact whole number or decimal

Area measures the enclosed region in square units, not the boundary length

A triangle has half the area of a parallelogram with the same base and perpendicular height

Halving the base-height product accounts for the triangular region

Keep two decimal places when the exact result needs them

Use the full decimal product for a parallelogram

A parallelogram-shaped panel has base b of 10.5 m and perpendicular height h of 5.2 m

The marked height meets the chosen base at a right angle

Calculate the area in m². Give an exact whole number or decimal

Area measures the enclosed region in square units, not the boundary length

Use the base and perpendicular height, not a sloping side

Changing a sloping side does not change this area if the base and perpendicular height stay fixed

Combine an outside height with decimal dimensions

Use matching length units before finding area

If a base is stated in metres and its height in centimetres, first write both lengths in metres

Divide a length in centimetres by one hundred to express it in metres

Now multiply the metre dimensions and report square metres

Do not multiply the metre number directly by the centimetre number and label that product square metres

A whole square metre contains one hundred centimetres in each direction

Converting a length uses a factor of one hundred here; converting an area uses a factor of ten thousand. These questions convert the length before calculating area

Convert the rectangle width before multiplying

A rectangular panel has length l of 8 m and perpendicular width w of 350 cm

The base and height are the rectangle length and width

Calculate the area in m². Give an exact whole number or decimal

Area measures the enclosed region in square units, not the boundary length

Convert the perpendicular height to metres before multiplying

Use the rectangle length and its perpendicular width

Length multiplied by width counts the square units across all rows

Read centimetres and metres as different length units

Convert the height, multiply, then halve

A triangular panel has base b of 9 m and perpendicular height h of 400 cm

The marked height meets the chosen base at a right angle

Calculate the area in m². Give an exact whole number or decimal

Area measures the enclosed region in square units, not the boundary length

Convert the perpendicular height to metres before multiplying

A triangle has half the area of a parallelogram with the same base and perpendicular height

Halving the base-height product accounts for the triangular region

Combine a decimal base with a centimetre height

Convert an outside height without lengthening the base

A parallelogram-shaped panel has base b of 8 m and perpendicular height h of 500 cm

The perpendicular height meets the extended base outside the panel

Calculate the area in m². Give an exact whole number or decimal

Area measures the enclosed region in square units, not the boundary length

Convert the perpendicular height to metres before multiplying

Use the base and perpendicular height, not a sloping side

Changing a sloping side does not change this area if the base and perpendicular height stay fixed

Report the whole parallelogram area in square metres

Identify the region, match the height and calculate in square units

Area measures a region in square units; perimeter measures its boundary in length units

Cutting and rearranging a parallelogram into a rectangle preserves area

Two identical triangles make a parallelogram with the same base and perpendicular height

The height is perpendicular to the chosen base or its extension. A sloping side is not a substitute

Use matching length units, multiply exactly, halve only for the triangle and report the correct square unit