Area, Perimeter and composite shapes (Area of a composite shape) Volume of a 3d shape and how to find the missing side of x

Area of a triangle

1/2 BH

The diagram shows the cross section of a solid metal shape with height 10cm, The top is 6cm, right is 6cm, left shows 12cm, bottom shows 12cm what is its volume? (Look at image for better understanding and solve)

1080cm³ Cut it into 3 parts so you have part A, B and C Find the area of all of them, add it together, and then times the answer by the height (which is 10) We got 3 as the height for the top shape because, the length if the whole shape is 12, and half of 12 is 6, and what number x 2 gives 6? it's 3 so 3 would be for there. So Find the half of the whole length, and the half of that or 1/4 x the length

Find the area of the composite shape (A square in the middle and two semi circles at both ends) Remember (Since it has 2 semi circles on both sides, there isn't a need to divide it by 2) The base is 20m the radius is 8m

Area of rectangle = 8 x 20 = 160 m ^ 2 Area of circle = pi(r ^ 2) 3.14 x 16 = 50.24cm^ 2 (Normally it would end here if there was only 1 semi circle in the composite shape but there are actually 2 on both sides) After add that to the area of the rectangle to find the complete answer

How to find area of a composite shape

Find the area for each shape... and then add all of them, then put cm2 or m2 ect at the end https://www.youtube.com/watch?v=z4Lat1uOQI4

How to find the volume of a composite shape

Find the area of each shape, Add the areas together Times the answer by the height.

Pythagoras theorem and how to find the missing side of X

If you have a triangle, the base is 3cm and the height is 4cm but you don't have the hypotenuse... You square the available angles then add them... (don't multiply anything yet) then when you get the sum you square it... After you find the root of the squared answer. Eg: C^2 =3cm^2 + 4cm ^ 2 (don't multiply just add and keep the square throughout the problem) C^2 = 9cm ^ 2 + 16cm ^2 C^2 = 25cm^2 Here for C^2 you square it again in order to have a square root above 25cm (C^2) ^2 = 25cm squared root = 5cm https://www.youtube.com/watch?v=tielQ3ejh70

Area of a square

LXL

Area of a rectangle (2d-flat)

LXW

Area of a rectangle (3d)

LXWXH

Are these shapes similar? (Showing a larger square and a smaller square next to it)

No, one is a square and the other is a rectangle. The cube has sides of 2cm... what effect does doubling the length have on... (Doubling = squaring) 1. The area of the base? A of square = L x L = 2cm x 2cm = 4cm^2 If we double the length of the sides the area is 4 x 4 = 16cm^2 B. The volume Volume of square = L X W X L 2 x 2 x 2 = 8cm ^ 3 Doubling 4 x 4 x 4 = 64cm^3

Area of a circle

Pi (r) ^2

Pythagorean Theorem

The area of the square of the hypotenuse is equal the sum of the area of the squares on the other two sides. The hypotenuse is the longest side of a triangle.

Volume of a cylinder

V=πr²h

Formula for Pythagoras theorem

a²+b²=c² b^2 + c^2 = a^2 C^2 + a^2 = b^2

area

cm2, m2 space inside a shape

volume

cm3, m3, How much can be held in a container

Find area of a composite shape questions

https://www.youtube.com/watch?v=1u2mGgPPtFs

How to find area of a composite shape with a circle as well

https://www.youtube.com/watch?v=2XYj-bnASCE 4:11 Remember the formula for the area of one semi-circle is the formula for the area of a circle divided by 2. So after finding the area of the circle, divide it by 2...

Rules for diameter

if you're required to find r squared and it shows a diameter, find the half of that diameter and square it to get r2..

hypotenuse

the side of a right triangle opposite the right angle