The area is the size of the surface and states the number of unit squares needed to completely cover that surface.

Shapes within shapes

Maths

In this unit, pupils built upon their prior learning of the area of different shapes. In the future unit, pupils will continue to further develop their understanding of shapes by considering surface area and volume of pyramids, spheres and cones.

In the prior unit, pupils derived the formula for the circumference and area of a circle. In this unit, this knowledge is combined with knowledge of fractions to find the arc length and area of a sector.

2D and 3D shape: compound shapes

A shape has a total area of 50 cm². Part of the shape is shaded. An area of 24 cm² is left unshaded. {{ }}% of the shape is shaded.

A shape has a total area of 45 cm².  Part of the shape is shaded. An area of 27 cm² is left unshaded. {{ }}% of the shape is shaded.

Which descriptors of this shape are correct?

The percentage of the shape which is shaded is {{ }}%.

$$\frac{10\times5}{9\times9+7\times12}\times100$$

$$\frac{9\times9+7\times12-10\times5}{9\times9+7\times12}\times100$$

$$\frac{10\times5}{9\times9+7\times12-10\times5}\times100$$

$$\frac{9\times9+7\times12-10\times5}{10\times5}\times100$$

Which calculation is correct to find the percentage of the rectilinear compound shape which is shaded?

This shape is made from a circle and the removal of two congruent circles. The percentage shaded in this shape is {{ }}%.

The area of a square with edge lengths of 1.4 cm is {{ }} cm².

The area of a circle with a diameter of 30 m is {{}}$$\pi$$ m².

Here are the first seven triangular numbers: 1, 3, 6, 10, 15, 21, 28. The next triangular number is {{}}.

The numbers 1, 4, 9, 16, 25, 36, 49, ...  are called the {{ }} numbers.

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