Area of rectangle 10 by 6 with a triangle on top height 4 Easy

The question

Question: find the area of this shape: a 10 by 6 rectangle with a triangle on top, 4 high.

1 Split into parts

This shape is made of simple shapes.

A dashed line splits it into a rectangle and a triangle.

The rectangle is 10 by 6.

The triangle sits on top.

Its base is the top of the rectangle: 10.

Its height is 4.

2 Area of each part

The rectangle: length times width.

10 times 6 is 60.

The triangle: half of base times height.

10 times 4 is 40.

Half of 40 means 40 divided by 2.

That is 20.

So the triangle is 20 square units.

3 Add the parts

The whole area is the two parts added.

60 plus 20 is 80.

So the area is 80 square units.

4 Check

Let's check another way.

Draw a box around the whole shape: 10 by 10.

Take away the two empty corners.

Each is half of a 5 by 4 box.

So together they are 5 × 4.

We get 80 again.

So the area is right!

Let's look back.

First: split into parts.

Then: area of each part.

Then: add the parts.

Last: check.

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Area of rectangle 10 cm by 6 cm with a semicircle on the end Medium

The question

Question: find the area of this shape: a 10 cm by 6 cm rectangle with a semicircle on one end.

1 Split into parts

This shape is made of simple shapes.

A dashed line splits off the round end.

The rectangle is 10 by 6.

The round end is a semicircle: half of a circle.

2 Area of each part

The rectangle: length times width.

10 times 6 is 60.

The semicircle sits on the end of the rectangle.

So its diameter is 6 cm.

The radius is half of it: 6 divided by 2 is 3.

The semicircle is half of a circle.

A circle is π times r squared.

So we take half.

3² means 3 times 3.

That is 9.

So it is half of π times 9.

Half of 9 is 4.5.

We write it as 4.5π.

3 Add the parts

The whole area is the two parts added: 60 + 4.5π.

We keep π in the answer.

That is the exact answer.

4 About how much

To see about how much, put 3.14 for π.

Forget the points: 45 times 314 is 14130.

Together, the numbers have 1 + 2 = 3 digits after the point.

So the answer has 3 too: 14.130, which is 14.13.

So we have 60 + 14.13.

60 plus 14.13 is 74.13.

So the area is about 74.13 cm².

5 Check

Let's check it makes sense.

The whole shape fits in a box 13 by 6: 78.

The area must be more than the rectangle alone: 60.

And less than the box: 78.

74.13 is between them.

So the answer makes sense!

Let's look back.

First: split into parts.

Then: area of each part.

Then: add the parts.

Then: about how much.

Last: check.

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Perimeter of rectangle 10 m by 6 m with a semicircle on the end Harder

The question

Question: find the perimeter of this shape: a 10 m by 6 m rectangle with a semicircle on one end.

1 Find the edge

The perimeter is the way all around the edge.

There are three straight sides and one round end.

Careful: the dashed line is inside the shape.

It is not on the edge, so we do not add it.

2 The round end

The semicircle sits on the end of the rectangle.

So its diameter is 6 m.

The radius is half of it: 6 divided by 2 is 3.

The round end is half of a circle.

The way round a circle is 2 times π times r.

We take half.

Half of 2 is 1.

So it is just π times 3.

We write it as 3π.

3 Add all the sides

Walk around: the top, the left side, the bottom, then the curve: 10 + 6 + 10 + 3π.

10 plus 6 plus 10 is 26.

So the perimeter is 26 + 3π.

We keep π in the answer.

That is the exact answer.

4 About how much

To see about how much, put 3.14 for π.

3 times 3.14 is 9.42.

26 plus 9.42 is 35.42.

So the perimeter is about 35.42 m.

5 Check

Let's check it makes sense.

The round end is 9.42.

It is longer than the straight line across it: 6.

It is shorter than going around the box corners: 3 + 6 + 3 = 12.

So the answer makes sense!

Let's look back.

First: find the edge.

Then: the round end.

Then: add all the sides.

Then: about how much.

Last: check.

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