Question

The diagram shows a triangle

inside a rectangle. All lengths are in cm.
Work out the area of the rectangle:
15
20
16

Answer 1

AREA RECTANGLE =300 cm²

Explanation:

If 2 of the 3 vertices of a triangle match up with 2 of the 4 vertices of a rectangle,then the area of the triangle will be exactly half of the area of the rectangle

(Or the area of the rectangle will be exactly double of the area of the triangle)

Area right triangle = ½ × base × height.

A = 1/2(15X20)

A=1/2( 300)

Area triangle =150

Area of rectangle is DOUBLE as the area of triangle

AREA RECTANGLE = 300

Answer 2

Area = 180 cm^2

Explanation:

See attached image. The width of the rectangle, a , is the hypotenuse of a right triangle with legs 15 and 20.

Use the Pythagorean Theorem: leg^2 +leg^2 = hypotenuse^2

`a^2=15^2+20^2\\\\a^2=225+400\\\\a^2=625\\\\a=√(625)=15`

The width, w, is one leg of a right triangle that has hypotenuse 20 and one leg 16.

`w^2+16^2=20^2\\\\w^2+256=400\\\\w^2=144\\\\w=√(144)=12`

The rectangle has length 15 cm and width 12 cm so its area is 12 x 15 = 180 cm^2